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Ramírez-Ávila GM, Kapitaniak T, Gonze D. Dynamical analysis of a periodically forced chaotic chemical oscillator. CHAOS (WOODBURY, N.Y.) 2024; 34:073154. [PMID: 39047162 DOI: 10.1063/5.0213913] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/14/2024] [Accepted: 07/11/2024] [Indexed: 07/27/2024]
Abstract
We present a comprehensive dynamical analysis of a chaotic chemical model referred to as the autocatalator, when subject to a periodic administration of one substrate. Our investigation encompasses the dynamical characterization of both unforced and forced systems utilizing isospikes and largest Lyapunov exponents-based parameter planes, bifurcation diagrams, and analysis of complex oscillations. Additionally, we present a phase diagram showing the effect of the period and amplitude of the forcing signal on the system's behavior. Furthermore, we show how the landscapes of parameter planes are altered in response to forcing application. This analysis contributes to a deeper understanding of the intricate dynamics induced by the periodic forcing of a chaotic system.
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Affiliation(s)
- Gonzalo Marcelo Ramírez-Ávila
- Namur Institute for Complex Systems (naXys), Université de Namur, Rue de Bruxelles 61, B-5000 Namur, Belgium
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
- Instituto de Investigaciones Físicas, and Planetario Max Schreier, Universidad Mayor de San Andrés, Campus Universitario, C. 27 s/n Cota-Cota, 0000 La Paz, Bolivia
- Unit of Theoretical Chronobiology, Université Libre de Bruxelles, CP231, Boulevard du Triomphe, 1050 Brussels, Belgium
| | - Tomasz Kapitaniak
- Division of Dynamics, Lodz University of Technology, Stefanowskiego 1/15, 90-924 Lodz, Poland
| | - Didier Gonze
- Unit of Theoretical Chronobiology, Université Libre de Bruxelles, CP231, Boulevard du Triomphe, 1050 Brussels, Belgium
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2
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Bartłomiejczyk P, Llovera Trujillo F, Signerska-Rynkowska J. Analysis of dynamics of a map-based neuron model via Lorenz maps. CHAOS (WOODBURY, N.Y.) 2024; 34:043110. [PMID: 38558045 DOI: 10.1063/5.0188464] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/21/2023] [Accepted: 03/09/2024] [Indexed: 04/04/2024]
Abstract
Modeling nerve cells can facilitate formulating hypotheses about their real behavior and improve understanding of their functioning. In this paper, we study a discrete neuron model introduced by Courbage et al. [Chaos 17, 043109 (2007)], where the originally piecewise linear function defining voltage dynamics is replaced by a cubic polynomial, with an additional parameter responsible for varying the slope. Showing that on a large subset of the multidimensional parameter space, the return map of the voltage dynamics is an expanding Lorenz map, we analyze both chaotic and periodic behavior of the system and describe the complexity of spiking patterns fired by a neuron. This is achieved by using and extending some results from the theory of Lorenz-like and expanding Lorenz mappings.
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Affiliation(s)
- Piotr Bartłomiejczyk
- Faculty of Applied Physics and Mathematics & BioTechMed Centre, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
| | - Frank Llovera Trujillo
- Doctoral School, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
| | - Justyna Signerska-Rynkowska
- Faculty of Applied Physics and Mathematics & BioTechMed Centre, Gdańsk University of Technology, Gabriela Narutowicza 11/12, 80-233 Gdańsk, Poland
- Dioscuri Centre in Topological Data Analysis, Institute of Mathematics of the Polish Academy of Sciences, Śniadeckich 8, 00-656 Warsaw, Poland
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3
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Nazari S, Jamshidi S. Efficient digital design of the nonlinear behavior of Hindmarsh-Rose neuron model in large-scale neural population. Sci Rep 2024; 14:3833. [PMID: 38360852 PMCID: PMC10869816 DOI: 10.1038/s41598-024-54525-8] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/05/2023] [Accepted: 02/13/2024] [Indexed: 02/17/2024] Open
Abstract
Spiking networks, as the third generation of neural networks, are of great interest today due to their low power consumption in cognitive processes. This important characteristic has caused the hardware implementation techniques of spiking networks in the form of neuromorphic systems attract a lot of attention. For the first time, the focus is on the digital implementation based on CORDIC approximation of the Hindmarsh-Rose (HR) neuron so that the hardware implementation cost is lower than previous studies. If the digital design of a neuron is done efficient, the possibility of implementing a population of neurons is provided for the feasibility of low-consumption implementation of high-level cognitive processes in hardware, which is considered in this paper through edge detector, noise removal and image magnification spiking networks based on the proposed CORDIC_HR model. While using less hardware resources, the proposed HR neuron model follows the behavior of the original neuron model in the time domain with much less error than previous study. Also, the complex nonlinear behavior of the original and the proposed model of HR neuron through the bifurcation diagram, phase space and nullcline space analysis under different system parameters was investigated and the good follow-up of the proposed model was confirmed from the original model. In addition to the fact that the individual behavior of the original and the proposed neurons is the same, the functional and behavioral performance of the randomly connected neuronal population of original and proposed neuron model is equal. In general, the main contribution of the paper is in presenting an efficient hardware model, which consumes less hardware resources, follows the behavior of the original model with high accuracy, and has an acceptable performance in image processing applications such as noise removal and edge detection.
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Affiliation(s)
- Soheila Nazari
- Faculty of Electrical Engineering, Shahid Beheshti University, Tehran, Iran.
| | - Shabnam Jamshidi
- Faculty of Electrical Engineering, Shahid Beheshti University, Tehran, Iran
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4
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Chen W, Mou Z, Xin Y, Li H, Wang T, Chen Y, Chen L, Yang BR, Chen Z, Luo Y, Liu GS. Self-Assembled Monolayer and Nanoparticles Coenhanced Fragmented Silver Nanowire Network Memristor. ACS APPLIED MATERIALS & INTERFACES 2024; 16:6057-6067. [PMID: 38285926 DOI: 10.1021/acsami.3c15351] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/31/2024]
Abstract
Silver nanowire (AgNW) networks with self-assembled structures and synaptic connectivity have been recently reported for constructing neuromorphic memristors. However, resistive switching at the cross-point junctions of the network is unstable due to locally enhanced Joule heating and the Gibbs-Thomson effect, which poses an obstacle to the integration of threshold switching and memory function in the same AgNW memristor. Here, fragmented AgNW networks combined with Ag nanoparticles (AgNPs) and mercapto self-assembled monolayers (SAMs) are devised to construct memristors with stable threshold switching and memory behavior. In the above design, the planar gaps between NW segments are for resistive switching, the AgNPs act as metal islands in the gaps to reduce threshold voltage (Vth) and holding voltage (Vhold), and the SAMs suppress surface atom diffusion to avoid Oswald ripening of the AgNPs, which improves switching stability. The fragmented NW-NP/SAM memristors not only circumvent the side effects of conventional NW-stacked junctions to provide durable threshold switching at >Vth but also exhibit synaptic characteristics such as long-term potentiation at ultralow voltage (≪Vth). The combination of NW segments, nanoparticles, and SAMs blazes a new trail for integrating artificial neurons and synapses in AgNW network memristors.
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Affiliation(s)
- Weizhen Chen
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
| | - Zongxia Mou
- Key Laboratory of Biomaterials of Guangdong Higher Education Institutes, Department of Biomedical Engineering, Jinan University, Guangzhou 510632, China
| | - Yijia Xin
- Department of Physics, Jinan University, Guangzhou 510632, China
| | - Haichuan Li
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
| | - Tianqi Wang
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
| | - Yaofei Chen
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
| | - Lei Chen
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
| | - Bo-Ru Yang
- State Key Laboratory of Optoelectronic Materials and Technologies, School of Electronics and Information Technology, Sun Yat-Sen University, Guangzhou 510006, China
| | - Zhe Chen
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
| | - Yunhan Luo
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
| | - Gui-Shi Liu
- Guangdong Provincial Key Laboratory of Optical Fiber Sensing and Communications, Key Laboratory of Visible Light Communications of Guangzhou, Key Laboratory of Optoelectronic Information and Sensing Technologies of Guangdong Higher Education Institutes, College of Physics & Optoelectronic Engineering, Jinan University, Guangzhou 510632, China
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5
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Yu F, Lin Y, Xu S, Yao W, Gracia YM, Cai S. Dynamic Analysis and FPGA Implementation of a New Fractional-Order Hopfield Neural Network System under Electromagnetic Radiation. Biomimetics (Basel) 2023; 8:559. [PMID: 38132498 PMCID: PMC10741897 DOI: 10.3390/biomimetics8080559] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2023] [Revised: 10/04/2023] [Accepted: 11/08/2023] [Indexed: 12/23/2023] Open
Abstract
Fractional calculus research indicates that, within the field of neural networks, fractional-order systems more accurately simulate the temporal memory effects present in the human brain. Therefore, it is worthwhile to conduct an in-depth investigation into the complex dynamics of fractional-order neural networks compared to integer-order models. In this paper, we propose a magnetically controlled, memristor-based, fractional-order chaotic system under electromagnetic radiation, utilizing the Hopfield neural network (HNN) model with four neurons as the foundation. The proposed system is solved by using the Adomain decomposition method (ADM). Then, through dynamic simulations of the internal parameters of the system, rich dynamic behaviors are found, such as chaos, quasiperiodicity, direction-controllable multi-scroll, and the emergence of analogous symmetric dynamic behaviors in the system as the radiation parameters are altered, with the order remaining constant. Finally, we implement the proposed new fractional-order HNN system on a field-programmable gate array (FPGA). The experimental results show the feasibility of the theoretical analysis.
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Affiliation(s)
- Fei Yu
- School of Computer and Communication Engineering, Changsha University of Science and Technology, Changsha 410114, China; (Y.L.); (S.X.); (W.Y.); (Y.M.G.); (S.C.)
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Lai Q, Wan Z, Zhang H, Chen G. Design and Analysis of Multiscroll Memristive Hopfield Neural Network With Adjustable Memductance and Application to Image Encryption. IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023; 34:7824-7837. [PMID: 35143405 DOI: 10.1109/tnnls.2022.3146570] [Citation(s) in RCA: 11] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Memristor is an ideal electronic device used as an artificial nerve synapse due to its unique memory function. This article presents a design of a new Hopfield neural network (HNN) that can generate multiscroll attractors by utilizing a new memristor as a synapse in the HNN. Differing from the others, this memristor is constructed with hyperbolic tangent functions. Taking the memristor as a self-feedback synapse of a neuron in the HNN, the memristive HNN can yield multidouble-scroll attractors, and its parameters can be used to effectively control the number of double scrolls contained in an attractor. Interestingly, the generation of multidouble-scroll attractors is independent of the memductance function but depends only on the internal state equation. Thus, the memductance function can be adjusted to yield various complex dynamical behaviors. Moreover, amplitude control effects and quantitatively controllable multistability are revealed by numerical analysis. The accurate reproduction of some dynamical behaviors by a designed circuit verifies the correctness of the numerical analysis. Finally, based on the proposed memristive HNN, a novel image encryption scheme in the 3-D setting is designed and evaluated, demonstrating its good encryption performances.
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Jaquette J, Kedia S, Sander E, Touboul JD. Reliability and robustness of oscillations in some slow-fast chaotic systems. CHAOS (WOODBURY, N.Y.) 2023; 33:103135. [PMID: 37874881 PMCID: PMC10599791 DOI: 10.1063/5.0166846] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/07/2023] [Accepted: 09/26/2023] [Indexed: 10/26/2023]
Abstract
A variety of nonlinear models of biological systems generate complex chaotic behaviors that contrast with biological homeostasis, the observation that many biological systems prove remarkably robust in the face of changing external or internal conditions. Motivated by the subtle dynamics of cell activity in a crustacean central pattern generator (CPG), this paper proposes a refinement of the notion of chaos that reconciles homeostasis and chaos in systems with multiple timescales. We show that systems displaying relaxation cycles while going through chaotic attractors generate chaotic dynamics that are regular at macroscopic timescales and are, thus, consistent with physiological function. We further show that this relative regularity may break down through global bifurcations of chaotic attractors such as crises, beyond which the system may also generate erratic activity at slow timescales. We analyze these phenomena in detail in the chaotic Rulkov map, a classical neuron model known to exhibit a variety of chaotic spike patterns. This leads us to propose that the passage of slow relaxation cycles through a chaotic attractor crisis is a robust, general mechanism for the transition between such dynamics. We validate this numerically in three other models: a simple model of the crustacean CPG neural network, a discrete cubic map, and a continuous flow.
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Affiliation(s)
| | | | - Evelyn Sander
- Department of Mathematical Sciences, George Mason University, Fairfax, Virginia 22030, USA
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Fu S, Yao Z, Qian C, Wang X. Star Memristive Neural Network: Dynamics Analysis, Circuit Implementation, and Application in a Color Cryptosystem. ENTROPY (BASEL, SWITZERLAND) 2023; 25:1261. [PMID: 37761560 PMCID: PMC10529167 DOI: 10.3390/e25091261] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Revised: 08/16/2023] [Accepted: 08/23/2023] [Indexed: 09/29/2023]
Abstract
At present, memristive neural networks with various topological structures have been widely studied. However, the memristive neural network with a star structure has not been investigated yet. In order to investigate the dynamic characteristics of neural networks with a star structure, a star memristive neural network (SMNN) model is proposed in this paper. Firstly, an SMNN model is proposed based on a Hopfield neural network and a flux-controlled memristor. Then, its chaotic dynamics are analyzed by using numerical analysis methods including bifurcation diagrams, Lyapunov exponents, phase plots, Poincaré maps, and basins of attraction. The results show that the SMNN can generate complex dynamical behaviors such as chaos, multi-scroll attractors, and initial boosting behavior. The number of multi-scroll attractors can be changed by adjusting the memristor's control parameters. And the position of the coexisting chaotic attractors can be changed by switching the memristor's initial values. Meanwhile, the analog circuit of the SMNN is designed and implemented. The theoretical and numerical results are verified through MULTISIM simulation results. Finally, a color image encryption scheme is designed based on the SMNN. Security performance analysis shows that the designed cryptosystem has good security.
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Affiliation(s)
- Sen Fu
- College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China
- Aircraft Technology Branch of Hunan Aerospace Co., Ltd., Changsha 410000, China
- China Aerospace Science and Industry Corporation, Beijing 100048, China
| | - Zhengjun Yao
- College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China
| | - Caixia Qian
- College of Materials Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing 211100, China
- Aircraft Technology Branch of Hunan Aerospace Co., Ltd., Changsha 410000, China
| | - Xia Wang
- Aircraft Technology Branch of Hunan Aerospace Co., Ltd., Changsha 410000, China
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9
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Eftekhari L, Amirian MM. Stability analysis of fractional order memristor synapse-coupled hopfield neural network with ring structure. Cogn Neurodyn 2023; 17:1045-1059. [PMID: 37522036 PMCID: PMC10374511 DOI: 10.1007/s11571-022-09844-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/26/2021] [Revised: 06/15/2022] [Accepted: 06/24/2022] [Indexed: 11/25/2022] Open
Abstract
A memristor is a nonlinear two-terminal electrical element that incorporates memory features and nanoscale properties, enabling us to design very high-density artificial neural networks. To enhance the memory property, we should use mathematical frameworks like fractional calculus, which is capable of doing so. Here, we first present a fractional-order memristor synapse-coupling Hopfield neural network on two neurons and then extend the model to a neural network with a ring structure that consists of n sub-network neurons, increasing the synchronization in the network. Necessary and sufficient conditions for the stability of equilibrium points are investigated, highlighting the dependency of the stability on the fractional-order value and the number of neurons. Numerical simulations and bifurcation analysis, along with Lyapunov exponents, are given in the two-neuron case that substantiates the theoretical findings, suggesting possible routes towards chaos when the fractional order of the system increases. In the n-neuron case also, it is revealed that the stability depends on the structure and number of sub-networks.
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Affiliation(s)
- Leila Eftekhari
- Department of Mathematics, Tarbiat Modares University, Tehran, IR 14117-13116 Iran
| | - Mohammad M. Amirian
- Department of Mathematics and Statistics, Dalhousie University, Halifax, NS CA B3H4R2 Canada
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Gyllingberg L, Szorkovszky A, Sumpter DJT. Using neuronal models to capture burst-and-glide motion and leadership in fish. J R Soc Interface 2023; 20:20230212. [PMID: 37464800 DOI: 10.1098/rsif.2023.0212] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2023] [Accepted: 06/28/2023] [Indexed: 07/20/2023] Open
Abstract
While mathematical models, in particular self-propelled particle models, capture many properties of large fish schools, they do not always capture the interactions of smaller shoals. Nor do these models tend to account for the use of intermittent locomotion, often referred to as burst-and-glide, by many species. In this paper, we propose a model of social burst-and-glide motion by combining a well-studied model of neuronal dynamics, the FitzHugh-Nagumo model, with a model of fish motion. We first show that our model can capture the motion of a single fish swimming down a channel. Extending to a two-fish model, where visual stimulus of a neighbour affects the internal burst or glide state of the fish, we observe a rich set of dynamics found in many species. These include: leader-follower behaviour; periodic changes in leadership; apparently random (i.e. chaotic) leadership change; and tit-for-tat turn taking. Moreover, unlike previous studies where a randomness is required for leadership switching to occur, we show that this can instead be the result of deterministic interactions. We give several empirically testable predictions for how bursting fish interact and discuss our results in light of recently established correlations between fish locomotion and brain activity.
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Affiliation(s)
| | - Alex Szorkovszky
- RITMO Centre for Interdisciplinary Studies in Rhythm, Time and Motion, University of Oslo, Oslo, Norway
| | - David J T Sumpter
- Department of Information Technology, Uppsala University, Uppsala, Sweden
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Lai Q, Guo S. Simple cyclic memristive neural networks with coexisting attractors and large-scale amplitude control. CHAOS (WOODBURY, N.Y.) 2023; 33:073153. [PMID: 37499247 DOI: 10.1063/5.0153885] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/12/2023] [Accepted: 07/06/2023] [Indexed: 07/29/2023]
Abstract
The memristor's unique memory function and non-volatile nature make it an ideal electronic bionic device for artificial neural synapses. This paper aims to construct a class of memristive neural networks (MNNs) with a simple circular connection relationship and complex dynamics by introducing a generic memristor as synapse. For placing the memristive synapse in different coupling positions, three MNNs with the same coupling cyclic connection are yielded. One remarkable feature of the proposed MNNs is that they can yield complex dynamics, in particular, abundant coexisting attractors and large-scale parameter-relied amplitude control, by comparing with some existing MNNs. Taking one of the MNNs as an example, the complex dynamics (including chaos, period-doubling bifurcation, symmetric coexisting attractors, large-scale amplitude control) and circuit implementation are studied . The number of equilibria and their stabilities are discussed. The parameter-relied dynamic evolution and the coexisting attractors are numerically shown by using bifurcations and phase portraits. A microcontroller-based hardware circuit is given to realize the network, which verifies the correctness of the numerical results and experimental results.
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Affiliation(s)
- Qiang Lai
- School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China
| | - Shicong Guo
- School of Electrical and Automation Engineering, East China Jiaotong University, Nanchang 330013, China
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12
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Guisande N, di Nunzio MP, Martinez N, Rosso OA, Montani F. Chaotic dynamics of the Hénon map and neuronal input-output: A comparison with neurophysiological data. CHAOS (WOODBURY, N.Y.) 2023; 33:043111. [PMID: 37097953 DOI: 10.1063/5.0142773] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/17/2023] [Accepted: 03/10/2023] [Indexed: 06/19/2023]
Abstract
In this study, the Hénon map was analyzed using quantifiers from information theory in order to compare its dynamics to experimental data from brain regions known to exhibit chaotic behavior. The goal was to investigate the potential of the Hénon map as a model for replicating chaotic brain dynamics in the treatment of Parkinson's and epilepsy patients. The dynamic properties of the Hénon map were compared with data from the subthalamic nucleus, the medial frontal cortex, and a q-DG model of neuronal input-output with easy numerical implementation to simulate the local behavior of a population. Using information theory tools, Shannon entropy, statistical complexity, and Fisher's information were analyzed, taking into account the causality of the time series. For this purpose, different windows over the time series were considered. The findings revealed that neither the Hénon map nor the q-DG model could perfectly replicate the dynamics of the brain regions studied. However, with careful consideration of the parameters, scales, and sampling used, they were able to model some characteristics of neural activity. According to these results, normal neural dynamics in the subthalamic nucleus region may present a more complex spectrum within the complexity-entropy causality plane that cannot be represented by chaotic models alone. The dynamic behavior observed in these systems using these tools is highly dependent on the studied temporal scale. As the size of the sample studied increases, the dynamics of the Hénon map become increasingly different from those of biological and artificial neural systems.
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Affiliation(s)
- Natalí Guisande
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
| | - Monserrat Pallares di Nunzio
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
| | - Nataniel Martinez
- Instituto de Física de Mar del Plata, Universidad Nacional de Mar del Plata & CONICET, Mar del Plata 7600, Buenos Aires, Argentina
| | - Osvaldo A Rosso
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
- Instituto de Física, Universidade Federal de Alagoas (UFAL), BR 104 Norte km 97, 57072-970 Maceió, Brazil
| | - Fernando Montani
- Instituto de Física de La Plata (IFLP), Universidad Nacional de La Plata, CONICET CCT-La Plata, Diagonal 113 entre 63 y 64, La Plata 1900, Buenos Aires, Argentina
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Topal I, Eroglu D. Reconstructing Network Dynamics of Coupled Discrete Chaotic Units from Data. PHYSICAL REVIEW LETTERS 2023; 130:117401. [PMID: 37001085 DOI: 10.1103/physrevlett.130.117401] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/20/2022] [Revised: 02/17/2023] [Accepted: 02/21/2023] [Indexed: 06/19/2023]
Abstract
Reconstructing network dynamics from data is crucial for predicting the changes in the dynamics of complex systems such as neuron networks; however, previous research has shown that the reconstruction is possible under strong constraints such as the need for lengthy data or small system size. Here, we present a recovery scheme blending theoretical model reduction and sparse recovery to identify the governing equations and the interactions of weakly coupled chaotic maps on complex networks, easing unrealistic constraints for real-world applications. Learning dynamics and connectivity lead to detecting critical transitions for parameter changes. We apply our technique to realistic neuronal systems with and without noise on a real mouse neocortex and artificial networks.
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Affiliation(s)
- Irem Topal
- Faculty of Engineering and Natural Sciences, Kadir Has University, 34083 Istanbul, Turkey
| | - Deniz Eroglu
- Faculty of Engineering and Natural Sciences, Kadir Has University, 34083 Istanbul, Turkey
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Silva S, Ribeiro F, Figueira V, Pinho F. Methodological Considerations in the Kinematic and Kinetic Analysis of Human Movement among Healthy Adolescents: A Scoping Review of Nonlinear Measures in Data Processing. SENSORS (BASEL, SWITZERLAND) 2022; 23:304. [PMID: 36616902 PMCID: PMC9823368 DOI: 10.3390/s23010304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/22/2022] [Accepted: 12/24/2022] [Indexed: 06/17/2023]
Abstract
Nonlinear measures have increasingly revealed the quality of human movement and its behaviour over time. Further analyses of human movement in real contexts are crucial for understanding its complex dynamics. The main objective was to identify and summarize the nonlinear measures used in data processing during out-of-laboratory assessments of human movement among healthy adolescents. Summarizing the methodological considerations was the secondary objective. The inclusion criteria were as follows: According to the Population, Concept, and Context (PCC) framework, healthy teenagers between 10 and 19 years old that reported kinetic and/or kinematic nonlinear data-processing measurements related to human movement in non-laboratory settings were included. PRISMA-ScR was used to conduct this review. PubMed, Science Direct, the Web of Science, and Google Scholar were searched. Studies published between the inception of the database and March 2022 were included. In total, 10 of the 2572 articles met the criteria. The nonlinear measures identified included entropy (n = 8), fractal analysis (n = 3), recurrence quantification (n = 2), and the Lyapunov exponent (n = 2). In addition to walking (n = 4) and swimming (n = 2), each of the remaining studies focused on different motor tasks. Entropy measures are preferred when studying the complexity of human movement, especially multiscale entropy, with authors also carefully combining different measures, namely entropy and fractal analysis.
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Affiliation(s)
- Sandra Silva
- Escola Superior de Saúde do Vale do Ave, Cooperativa de Ensino Superior Politécnico e Universitário, Rua José António Vidal, 81, 4760-409 Vila Nova de Famalicão, Portugal
- School of Health Sciences, University of Aveiro, 3810-193 Aveiro, Portugal
- Department of Medical Sciences, University of Aveiro, 3810-193 Aveiro, Portugal
| | - Fernando Ribeiro
- School of Health Sciences, University of Aveiro, 3810-193 Aveiro, Portugal
- Institute of Biomedicine—iBiMED, University of Aveiro, 3810-193 Aveiro, Portugal
| | - Vânia Figueira
- Escola Superior de Saúde do Vale do Ave, Cooperativa de Ensino Superior Politécnico e Universitário, Rua José António Vidal, 81, 4760-409 Vila Nova de Famalicão, Portugal
- Research Centre in Physical Activity, Health and Leisure, Faculty of Sport, University of Porto, Rua Dr. Plácido da Costa, 91, 4200-450 Porto, Portugal
| | - Francisco Pinho
- Escola Superior de Saúde do Vale do Ave, Cooperativa de Ensino Superior Politécnico e Universitário, Rua José António Vidal, 81, 4760-409 Vila Nova de Famalicão, Portugal
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15
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Nezhad Hajian D, Parthasarathy S, Parastesh F, Rajagopal K, Jafari S. Dominant Attractor in Coupled Non-Identical Chaotic Systems. ENTROPY (BASEL, SWITZERLAND) 2022; 24:1807. [PMID: 36554212 PMCID: PMC9778076 DOI: 10.3390/e24121807] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 11/30/2022] [Accepted: 12/09/2022] [Indexed: 06/17/2023]
Abstract
The dynamical interplay of coupled non-identical chaotic oscillators gives rise to diverse scenarios. The incoherent dynamics of these oscillators lead to the structural impairment of attractors in phase space. This paper investigates the couplings of Lorenz-Rössler, Lorenz-HR, and Rössler-HR to identify the dominant attractor. By dominant attractor, we mean the attractor that is less changed by coupling. For comparison and similarity detection, a cost function based on the return map of the coupled systems is used. The possible effects of frequency and amplitude differences between the systems on the results are also examined. Finally, the inherent chaotic characteristic of systems is compared by computing the largest Lyapunov exponent. The results suggest that in each coupling case, the attractor with the greater largest Lyapunov exponent is dominant.
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Affiliation(s)
- Dorsa Nezhad Hajian
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
| | - Sriram Parthasarathy
- Centre for Computational Modelling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
- Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, Iran
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16
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Aoun MA. Resonant neuronal groups. PHYSICS OPEN 2022; 13:100104. [DOI: 10.1016/j.physo.2022.100104] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
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17
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Parker JE, Short KM. Cupolets in a chaotic neuron model. CHAOS (WOODBURY, N.Y.) 2022; 32:113104. [PMID: 36456317 DOI: 10.1063/5.0101667] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/02/2022] [Accepted: 09/26/2022] [Indexed: 06/17/2023]
Abstract
This paper reports the first finding of cupolets in a chaotic Hindmarsh-Rose neural model. Cupolets (chaotic, unstable, periodic, orbit-lets) are unstable periodic orbits that have been stabilized through a particular control scheme by applying a binary control sequence. We demonstrate different neural dynamics (periodic or chaotic) of the Hindmarsh-Rose model through a bifurcation diagram where the external input current, I, is the bifurcation parameter. We select a region in the chaotic parameter space and provide the results of numerical simulations. In this chosen parameter space, a control scheme is applied when the trajectory intersects with either of the two control planes. The type of the control is determined by a bit in a binary control sequence. The control is either a small microcontrol (0) or a large macrocontrol (1) that adjusts the future dynamics of the trajectory by a perturbation determined by the coding function r ( x ). We report the discovery of many cupolets with corresponding control sequences and comment on the differences with previously reported cupolets in the double scroll system. We provide some examples of the generated cupolets and conclude by discussing potential implications for biological neurons.
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Affiliation(s)
- John E Parker
- Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire, Durham, New Hampshire 03824, USA
| | - Kevin M Short
- Integrated Applied Mathematics Program, Department of Mathematics and Statistics, University of New Hampshire, Durham, New Hampshire 03824, USA
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18
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Harikrishnan NB, Pranay SY, Nagaraj N. Classification of SARS-CoV-2 viral genome sequences using Neurochaos Learning. Med Biol Eng Comput 2022; 60:2245-2255. [PMID: 35668230 PMCID: PMC9170350 DOI: 10.1007/s11517-022-02591-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/27/2021] [Accepted: 04/28/2022] [Indexed: 12/01/2022]
Abstract
Abstract The high spread rate of SARS-CoV-2 virus has put the researchers all over the world in a demanding situation. The need of the hour is to develop novel learning algorithms that can effectively learn a general pattern by training with fewer genome sequences of coronavirus. Learning from very few training samples is necessary and important during the beginning of a disease outbreak when sequencing data is limited. This is because a successful detection and isolation of patients can curb the spread of the virus. However, this poses a huge challenge for machine learning and deep learning algorithms as they require huge amounts of training data to learn the pattern and distinguish from other closely related viruses. In this paper, we propose a new paradigm – Neurochaos Learning (NL) for classification of coronavirus genome sequence that addresses this specific problem. NL is inspired from the empirical evidence of chaos and non-linearity at the level of neurons in biological neural networks. The average sensitivity, specificity and accuracy for NL are 0.998, 0.999 and 0.998 respectively for the multiclass classification problem (SARS-CoV-2, Coronaviridae, Metapneumovirus, Rhinovirus and Influenza) using leave one out crossvalidation. With just one training sample per class for 1000 independent random trials of training, we report an average macro F1-score \documentclass[12pt]{minimal}
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\begin{document}$$> 0.99$$\end{document}>0.99 for the classification of SARS-CoV-2 from SARS-CoV-1 genome sequences. We compare the performance of NL with K-nearest neighbours (KNN), logistic regression, random forest, SVM, and naïve Bayes classifiers. We foresee promising future applications in genome classification using NL with novel combinations of chaotic feature engineering and other machine learning algorithms. Graphical abstract ![]()
Supplementary Information The online version contains supplementary material available at 10.1007/s11517-022-02591-3.
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Affiliation(s)
- N. B. Harikrishnan
- The University of Trans-Disciplinary Health Sciences and Technology, Bengaluru, 560064 Karnataka India
- Consciousness Studies Programme, National Institute of Advanced Studies, Indian Institute of Science Campus, Bengaluru, 560012 Karnataka India
| | - S. Y. Pranay
- Consciousness Studies Programme, National Institute of Advanced Studies, Indian Institute of Science Campus, Bengaluru, 560012 Karnataka India
| | - Nithin Nagaraj
- Consciousness Studies Programme, National Institute of Advanced Studies, Indian Institute of Science Campus, Bengaluru, 560012 Karnataka India
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19
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From chaos to clock in recurrent neural net. Case study. Biosystems 2022; 220:104739. [PMID: 35868428 DOI: 10.1016/j.biosystems.2022.104739] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/24/2022] [Revised: 07/14/2022] [Accepted: 07/14/2022] [Indexed: 11/24/2022]
Abstract
What is the reason for complex dynamical patterns registered from real biological neuronal networks? Noise and dynamical reconfiguring of a network (functional/dynamic connectome) were proposed as possible answers. In this case study, we report a complex dynamical pattern observed in a simple deterministic network of 25 excitatory neurons with fixed connectome. After a short initial stimulation, the network is engaged into a complex dynamics, which lasts for a long time. Eventually, with no external intervention, the dynamics comes to a periodic one with a short period. The long transient is positively checked for being chaotic. We conclude that the complex dynamics observed is the output of neural computation performed in the process of neuronal firings and spikes propagation.
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20
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Zhang X, Chen G. A simple topological model for two coupled neurons. CHAOS (WOODBURY, N.Y.) 2022; 32:073124. [PMID: 35907729 DOI: 10.1063/5.0097385] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/28/2022] [Accepted: 06/20/2022] [Indexed: 06/15/2023]
Abstract
A simple topological model describing the chaotic dynamics of two coupled neurons is established and analyzed based on the Smale horseshoe theory.
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Affiliation(s)
- Xu Zhang
- Department of Mathematics, Shandong University, Weihai 264209, Shandong, China
| | - Guanrong Chen
- Department of Electrical Engineering, City University of Hong Kong, Hong Kong SAR, China
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21
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Araújo NS, Reyes-Garcia SZ, Brogin JAF, Bueno DD, Cavalheiro EA, Scorza CA, Faber J. Chaotic and stochastic dynamics of epileptiform-like activities in sclerotic hippocampus resected from patients with pharmacoresistant epilepsy. PLoS Comput Biol 2022; 18:e1010027. [PMID: 35417449 PMCID: PMC9037954 DOI: 10.1371/journal.pcbi.1010027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2021] [Revised: 04/25/2022] [Accepted: 03/16/2022] [Indexed: 11/30/2022] Open
Abstract
The types of epileptiform activity occurring in the sclerotic hippocampus with highest incidence are interictal-like events (II) and periodic ictal spiking (PIS). These activities are classified according to their event rates, but it is still unclear if these rate differences are consequences of underlying physiological mechanisms. Identifying new and more specific information related to these two activities may bring insights to a better understanding about the epileptogenic process and new diagnosis. We applied Poincaré map analysis and Recurrence Quantification Analysis (RQA) onto 35 in vitro electrophysiological signals recorded from slices of 12 hippocampal tissues surgically resected from patients with pharmacoresistant temporal lobe epilepsy. These analyzes showed that the II activity is related to chaotic dynamics, whereas the PIS activity is related to deterministic periodic dynamics. Additionally, it indicates that their different rates are consequence of different endogenous dynamics. Finally, by using two computational models we were able to simulate the transition between II and PIS activities. The RQA was applied to different periods of these simulations to compare the recurrences between artificial and real signals, showing that different ranges of regularity-chaoticity can be directly associated with the generation of PIS and II activities. Temporal lobe epilepsy (TLE) is the most prevalent type of epilepsy in adults and hippocampal sclerosis is the major pathophysiological substrate of pharmaco-refractory TLE. Different patterns of epileptiform-like activity have been described in human hippocampal sclerosis, but the standard analysis applied to characterize the activities usually do not consider the nonlinear features that epileptiform patterns exhibit. Here, using Poincaré map and Recurrence Quantitative Analysis we characterized the most prevalent type of epileptiform-like activities—interictal-like events (II) and periodic ictal spiking (PIS), recorded in vitro from resected hippocampi of pharmacoresistant patients with TLE—according to their levels of stochasticity, chaoticity and determinism. The II activities showed to be more chaotic with complex rhythmicity than PIS activities. The nonlinear dynamic differences between II and PIS leads us to conjecture that they are expressions of different seizure susceptibility. We also identified that each hippocampal subfield expresses II and PIS activities in a specific and different way. Finally, from the modulation of internal parameters of two computational models, we show the conversion of one type of activity into the other, showing how specific neuron networks synchronize over time, leading to II and PIS activities and then into a generalized seizure.
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Affiliation(s)
- Noemi S. Araújo
- Department of Neurology and Neurosurgery, Federal University of São Paulo (UNIFESP), São Paulo, São Paulo, Brazil
| | - Selvin Z. Reyes-Garcia
- Departamento de Ciencias Morfológicas, Facultad de Ciencias Médicas, Universidad Nacional Autónoma de Honduras, Tegucigalpa, Honduras
| | - João A. F. Brogin
- Department of Mechanical Engineering, São Paulo State University (UNESP), School of Engineering of Ilha Solteira, Ilha Solteira, São Paulo, Brazil
| | - Douglas D. Bueno
- Department of Mathematics, São Paulo State University (UNESP), School of Engineering of Ilha Solteira, Ilha Solteira, São Paulo, Brazil
| | - Esper A. Cavalheiro
- Department of Neurology and Neurosurgery, Federal University of São Paulo (UNIFESP), São Paulo, São Paulo, Brazil
| | - Carla A. Scorza
- Department of Neurology and Neurosurgery, Federal University of São Paulo (UNIFESP), São Paulo, São Paulo, Brazil
| | - Jean Faber
- Department of Neurology and Neurosurgery, Federal University of São Paulo (UNIFESP), São Paulo, São Paulo, Brazil
- * E-mail:
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22
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Toker D, Pappas I, Lendner JD, Frohlich J, Mateos DM, Muthukumaraswamy S, Carhart-Harris R, Paff M, Vespa PM, Monti MM, Sommer FT, Knight RT, D'Esposito M. Consciousness is supported by near-critical slow cortical electrodynamics. Proc Natl Acad Sci U S A 2022; 119:e2024455119. [PMID: 35145021 PMCID: PMC8851554 DOI: 10.1073/pnas.2024455119] [Citation(s) in RCA: 46] [Impact Index Per Article: 23.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2020] [Accepted: 12/20/2021] [Indexed: 12/21/2022] Open
Abstract
Mounting evidence suggests that during conscious states, the electrodynamics of the cortex are poised near a critical point or phase transition and that this near-critical behavior supports the vast flow of information through cortical networks during conscious states. Here, we empirically identify a mathematically specific critical point near which waking cortical oscillatory dynamics operate, which is known as the edge-of-chaos critical point, or the boundary between stability and chaos. We do so by applying the recently developed modified 0-1 chaos test to electrocorticography (ECoG) and magnetoencephalography (MEG) recordings from the cortices of humans and macaques across normal waking, generalized seizure, anesthesia, and psychedelic states. Our evidence suggests that cortical information processing is disrupted during unconscious states because of a transition of low-frequency cortical electric oscillations away from this critical point; conversely, we show that psychedelics may increase the information richness of cortical activity by tuning low-frequency cortical oscillations closer to this critical point. Finally, we analyze clinical electroencephalography (EEG) recordings from patients with disorders of consciousness (DOC) and show that assessing the proximity of slow cortical oscillatory electrodynamics to the edge-of-chaos critical point may be useful as an index of consciousness in the clinical setting.
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Affiliation(s)
- Daniel Toker
- Department of Psychology, University of California, Los Angeles, CA 90095;
| | - Ioannis Pappas
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Psychology, University of California, Berkeley, CA 94704
- Laboratory of Neuro Imaging, Stevens Institute for Neuroimaging and Informatics, Keck School of Medicine, University of Southern California, Los Angeles, CA 90033
| | - Janna D Lendner
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Anesthesiology and Intensive Care, University Medical Center, 72076 Tübingen, Germany
| | - Joel Frohlich
- Department of Psychology, University of California, Los Angeles, CA 90095
| | - Diego M Mateos
- Consejo Nacional de Investigaciones Científicas y Técnicas de Argentina, C1425 Buenos Aires, Argentina
- Facultad de Ciencia y Tecnología, Universidad Autónoma de Entre Ríos, E3202 Paraná, Entre Ríos, Argentina
- Grupo de Análisis de Neuroimágenes, Instituo de Matemática Aplicada del Litoral, S3000 Santa Fe, Argentina
| | - Suresh Muthukumaraswamy
- School of Pharmacy, Faculty of Medical and Health Sciences, The University of Auckland, 1010 Auckland, New Zealand
| | - Robin Carhart-Harris
- Neuropsychopharmacology Unit, Centre for Psychiatry, Imperial College London, London SW7 2AZ, United Kingdom
- Centre for Psychedelic Research, Department of Psychiatry, Imperial College London, London SW7 2AZ, United Kingdom
| | - Michelle Paff
- Department of Neurological Surgery, University of California, Irvine, CA 92697
| | - Paul M Vespa
- Brain Injury Research Center, Department of Neurosurgery, University of California, Los Angeles, CA 90095
| | - Martin M Monti
- Department of Psychology, University of California, Los Angeles, CA 90095
- Brain Injury Research Center, Department of Neurosurgery, University of California, Los Angeles, CA 90095
| | - Friedrich T Sommer
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94704
| | - Robert T Knight
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Psychology, University of California, Berkeley, CA 94704
| | - Mark D'Esposito
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA 94704
- Department of Psychology, University of California, Berkeley, CA 94704
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23
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Su E, Cai S, Xie L, Li H, Schultz T. STAnet: A Spatiotemporal Attention Network for Decoding Auditory Spatial Attention from EEG. IEEE Trans Biomed Eng 2022; 69:2233-2242. [PMID: 34982671 DOI: 10.1109/tbme.2022.3140246] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
OBJECTIVE Humans are able to localize the source of a sound. This enables them to direct attention to a particular speaker in a cocktail party. Psycho-acoustic studies show that the sensory cortices of the human brain respond to the location of sound sources differently, and the auditory attention itself is a dynamic and temporally based brain activity. In this work, we seek to build a computational model which uses both spatial and temporal information manifested in EEG signals for auditory spatial attention detection (ASAD). METHODS We propose an end-to-end spatiotemporal attention network, denoted as STAnet, to detect auditory spatial attention from EEG. The STAnet is designed to assign differentiated weights dynamically to EEG channels through a spatial attention mechanism, and to temporal patterns in EEG signals through a temporal attention mechanism. RESULTS We report the ASAD experiments on two publicly available datasets. The STAnet outperforms other competitive models by a large margin under various experimental conditions. Its attention decision for 1-second decision window outperforms that of the state-of-the-art techniques for 10-second decision window. Experimental results also demonstrate that the STAnet achieves competitive performance on EEG signals ranging from 64 to as few as 16 channels. CONCLUSION This study provides evidence suggesting that efficient low-density EEG online decoding is within reach. SIGNIFICANCE This study also marks an important step towards the practical implementation of ASAD in real life applications.
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24
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Gu H, Chou CA. Optimizing non-uniform multivariate embedding for multiscale entropy analysis of complex systems. Biomed Signal Process Control 2022. [DOI: 10.1016/j.bspc.2021.103206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/02/2022]
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25
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Su E, Cai S, Li P, Xie L, Li H. Auditory Attention Detection with EEG Channel Attention. ANNUAL INTERNATIONAL CONFERENCE OF THE IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. IEEE ENGINEERING IN MEDICINE AND BIOLOGY SOCIETY. ANNUAL INTERNATIONAL CONFERENCE 2021; 2021:5804-5807. [PMID: 34892439 DOI: 10.1109/embc46164.2021.9630508] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Auditory attention detection (AAD) seeks to detect the attended speech from EEG signals in a multi-talker scenario, i.e. cocktail party. As the EEG channels reflect the activities of different brain areas, a task-oriented channel selection technique improves the performance of brain-computer interface applications. In this study, we propose a soft channel attention mechanism, instead of hard channel selection, that derives an EEG channel mask by optimizing the auditory attention detection task. The neural AAD system consists of a neural channel attention mechanism and a convolutional neural network (CNN) classifier. We evaluate the proposed framework on a publicly available database. We achieve 88.3% and 77.2% for 2-second and 0.1-second decision windows with 64-channel EEG; and 86.1% and 83.9% for 2-second decision windows with 32-channel and 16-channel EEG, respectively. The proposed framework outperforms other competitive models by a large margin across all test cases.
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26
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Abrevaya G, Dumas G, Aravkin AY, Zheng P, Gagnon-Audet JC, Kozloski J, Polosecki P, Lajoie G, Cox D, Dawson SP, Cecchi G, Rish I. Learning Brain Dynamics With Coupled Low-Dimensional Nonlinear Oscillators and Deep Recurrent Networks. Neural Comput 2021; 33:2087-2127. [PMID: 34310676 DOI: 10.1162/neco_a_01401] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2020] [Accepted: 02/19/2021] [Indexed: 01/16/2023]
Abstract
Many natural systems, especially biological ones, exhibit complex multivariate nonlinear dynamical behaviors that can be hard to capture by linear autoregressive models. On the other hand, generic nonlinear models such as deep recurrent neural networks often require large amounts of training data, not always available in domains such as brain imaging; also, they often lack interpretability. Domain knowledge about the types of dynamics typically observed in such systems, such as a certain type of dynamical systems models, could complement purely data-driven techniques by providing a good prior. In this work, we consider a class of ordinary differential equation (ODE) models known as van der Pol (VDP) oscil lators and evaluate their ability to capture a low-dimensional representation of neural activity measured by different brain imaging modalities, such as calcium imaging (CaI) and fMRI, in different living organisms: larval zebrafish, rat, and human. We develop a novel and efficient approach to the nontrivial problem of parameters estimation for a network of coupled dynamical systems from multivariate data and demonstrate that the resulting VDP models are both accurate and interpretable, as VDP's coupling matrix reveals anatomically meaningful excitatory and inhibitory interactions across different brain subsystems. VDP outperforms linear autoregressive models (VAR) in terms of both the data fit accuracy and the quality of insight provided by the coupling matrices and often tends to generalize better to unseen data when predicting future brain activity, being comparable to and sometimes better than the recurrent neural networks (LSTMs). Finally, we demonstrate that our (generative) VDP model can also serve as a data-augmentation tool leading to marked improvements in predictive accuracy of recurrent neural networks. Thus, our work contributes to both basic and applied dimensions of neuroimaging: gaining scientific insights and improving brain-based predictive models, an area of potentially high practical importance in clinical diagnosis and neurotechnology.
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Affiliation(s)
- Germán Abrevaya
- Departamento de Física, FCEyN, UBA and IFIBA, CONICET, 1428 Buenos Aires, Argentina
| | - Guillaume Dumas
- Mila-Quebec Artificial Intelligence Institute, and CHU Sainte-Justine Research Center, Department of Psychiatry, Universitéde Montréal, Montreal H3A OE8, Canada
| | | | - Peng Zheng
- University of Washington, Seattle, WA 98195, U.S.A.
| | | | - James Kozloski
- IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
| | - Pablo Polosecki
- IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
| | - Guillaume Lajoie
- Mila-Quebec Artificial Intelligence Institute, Universitéde Montréal, Montreal H3A OE8, Canada
| | - David Cox
- MIT-IBM Watson AI Lab, Cambridge, MA 02139, U.S.A.
| | - Silvina Ponce Dawson
- Departamento de Física, FCEyN, UBA and IFIBA, CONICET, 1428 Buenos Aires, Argentina
| | - Guillermo Cecchi
- IBM T. J. Watson Research Center, Yorktown Heights, NY 10598, U.S.A.
| | - Irina Rish
- Mila-Quebec Artificial Intelligence Institute, Université de Montréal, Montreal H3A OE8, Canada
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27
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Shamsi E, Ahmadi-Pajouh MA, Seifi Ala T. Higuchi fractal dimension: An efficient approach to detection of brain entrainment to theta binaural beats. Biomed Signal Process Control 2021. [DOI: 10.1016/j.bspc.2021.102580] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/13/2023]
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28
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N B H, Nagaraj N. When Noise meets Chaos: Stochastic Resonance in Neurochaos Learning. Neural Netw 2021; 143:425-435. [PMID: 34252737 DOI: 10.1016/j.neunet.2021.06.025] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Revised: 05/17/2021] [Accepted: 06/24/2021] [Indexed: 10/21/2022]
Abstract
Chaos and Noise are ubiquitous in the Brain. Inspired by the chaotic firing of neurons and the constructive role of noise in neuronal models, we for the first time connect chaos, noise and learning. In this paper, we demonstrate Stochastic Resonance (SR) phenomenon in Neurochaos Learning (NL). SR manifests at the level of a single neuron of NL and enables efficient subthreshold signal detection. Furthermore, SR is shown to occur in single and multiple neuronal NL architecture for classification tasks - both on simulated and real-world spoken digit datasets, and in architectures with 1D chaotic maps as well as Hindmarsh-Rose spiking neurons. Intermediate levels of noise in neurochaos learning enable peak performance in classification tasks thus highlighting the role of SR in AI applications, especially in brain inspired learning architectures.
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Affiliation(s)
- Harikrishnan N B
- The University of Trans-Disciplinary Health Sciences And Technology, Bengaluru, India; Consciousness Studies Programme, National Institute of Advanced Studies, Indian Institute of Science Campus, Bengaluru, India.
| | - Nithin Nagaraj
- Consciousness Studies Programme, National Institute of Advanced Studies, Indian Institute of Science Campus, Bengaluru, India.
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29
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Baysal V, Erkan E, Yilmaz E. Impacts of autapse on chaotic resonance in single neurons and small-world neuronal networks. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2021; 379:20200237. [PMID: 33840215 DOI: 10.1098/rsta.2020.0237] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 10/08/2020] [Indexed: 05/22/2023]
Abstract
Chaotic resonance (CR) is a new phenomenon induced by an intermediate level of chaotic signal intensity in neuronal systems. In the current study, we investigated the effects of autapse on the CR phenomenon in single neurons and small-world (SW) neuronal networks. In single neurons, we assume that the neuron has only one autapse modelled as electrical, excitatory chemical and inhibitory chemical synapse, respectively. Then, we analysed the effects of each one on the CR, separately. Obtained results revealed that, regardless of its type, autapse significantly increases the chaotic resonance of the appropriate autaptic parameter's values. It is also observed that, at the optimal chaotic current intensity, the multiple CR emerges depending on autaptic time delay for all the autapse types when the autaptic delay time or its integer multiples match the half period or period of the weak signal. In SW networks, we investigated the effects of chaotic activity on the prorogation of pacemaker activity, where pacemaker neurons have different kinds of autapse as considered in single neuron cases. Obtained results revealed that excitatory and electrical autapses prominently increase the prorogation of pacemaker activity, whereas inhibitory autapse reduces or does not change it. Also, the best propagation was obtained when the autapse was excitatory. This article is part of the theme issue 'Vibrational and stochastic resonance in driven nonlinear systems (part 2)'.
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Affiliation(s)
- Veli Baysal
- Department of Computer Engineering, Bartın University, 74110 Bartın, Turkey
| | - Erdem Erkan
- Department of Computer Engineering, Bartın University, 74110 Bartın, Turkey
| | - Ergin Yilmaz
- Department of Biomedical Engineering, Zonguldak Bulent Ecevit University, 67100 Zonguldak, Turkey
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Abstract
AbstractThis paper explores current developments in evolutionary and bio-inspired approaches to autonomous robotics, concentrating on research from our group at the University of Sussex. These developments are discussed in the context of advances in the wider fields of adaptive and evolutionary approaches to AI and robotics, focusing on the exploitation of embodied dynamics to create behaviour. Four case studies highlight various aspects of such exploitation. The first exploits the dynamical properties of a physical electronic substrate, demonstrating for the first time how component-level analog electronic circuits can be evolved directly in hardware to act as robot controllers. The second develops novel, effective and highly parsimonious navigation methods inspired by the way insects exploit the embodied dynamics of innate behaviours. Combining biological experiments with robotic modeling, it is shown how rapid route learning can be achieved with the aid of navigation-specific visual information that is provided and exploited by the innate behaviours. The third study focuses on the exploitation of neuromechanical chaos in the generation of robust motor behaviours. It is demonstrated how chaotic dynamics can be exploited to power a goal-driven search for desired motor behaviours in embodied systems using a particular control architecture based around neural oscillators. The dynamics are shown to be chaotic at all levels in the system, from the neural to the embodied mechanical. The final study explores the exploitation of the dynamics of brain-body-environment interactions for efficient, agile flapping winged flight. It is shown how a multi-objective evolutionary algorithm can be used to evolved dynamical neural controllers for a simulated flapping wing robot with feathered wings. Results demonstrate robust, stable, agile flight is achieved in the face of random wind gusts by exploiting complex asymmetric dynamics partly enabled by continually changing wing and tail morphologies.
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Weistuch C, Mujica-Parodi LR, Dill K. The Refractory Period Matters: Unifying Mechanisms of Macroscopic Brain Waves. Neural Comput 2021; 33:1145-1163. [PMID: 33617741 DOI: 10.1162/neco_a_01371] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2020] [Accepted: 11/16/2020] [Indexed: 11/04/2022]
Abstract
The relationship between complex brain oscillations and the dynamics of individual neurons is poorly understood. Here we utilize maximum caliber, a dynamical inference principle, to build a minimal yet general model of the collective (mean field) dynamics of large populations of neurons. In agreement with previous experimental observations, we describe a simple, testable mechanism, involving only a single type of neuron, by which many of these complex oscillatory patterns may emerge. Our model predicts that the refractory period of neurons, which has often been neglected, is essential for these behaviors.
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Affiliation(s)
- Corey Weistuch
- Laufer Center for Physical and Quantitative Biology and Department of Applied Mathematics and Statistics, Stony Brook University, Stony Brook, NY 11794, U.S.A.
| | - Lilianne R Mujica-Parodi
- Laufer Center for Physical and Quantitative Biology, Departments of Biomedical Engineering and of Physics and Astronomy, Program in Neuroscience, and Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, U.S.A., and Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital and Harvard Medical School, Boston, MA 02129, U.S.A.
| | - Ken Dill
- Laufer Center for Physical and Quantitative Biology, Department of Physics and Astronomy, and Department of Chemistry, Stony Brook University, Stony Brook, NY 11794, U.S.A.
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32
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Serrano S, Martínez MA, Barrio R. Order in chaos: Structure of chaotic invariant sets of square-wave neuron models. CHAOS (WOODBURY, N.Y.) 2021; 31:043108. [PMID: 34251255 DOI: 10.1063/5.0043302] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/07/2021] [Accepted: 03/12/2021] [Indexed: 06/13/2023]
Abstract
Bursting phenomena and, in particular, square-wave or fold/hom bursting, are found in a wide variety of mathematical neuron models. These systems have different behavior regimes depending on the parameters, whether spiking, bursting, or chaotic. We study the topological structure of chaotic invariant sets present in square-wave bursting neuron models, first detailed using the Hindmarsh-Rose neuron model and later exemplary in the more realistic model of a leech heart neuron. We show that the unstable periodic orbits that form the skeleton of the chaotic invariant sets are deeply related to the spike-adding phenomena, typical from these models, and how there are specific symbolic sequences and a symbolic grammar that organize how and where the periodic orbits appear. Linking this information with the topological template analysis permits us to understand how the internal structure of the chaotic invariants is modified and how more symbolic sequences are allowed. Furthermore, the results allow us to conjecture that, for these systems, the limit template when the small parameter ε, which controls the slow gating variable, tends to zero is the complete Smale topological template.
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Affiliation(s)
- Sergio Serrano
- Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza, Spain
| | - M Angeles Martínez
- Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza, Spain
| | - Roberto Barrio
- Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza, Spain
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33
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Heltberg ML, Krishna S, Kadanoff LP, Jensen MH. A tale of two rhythms: Locked clocks and chaos in biology. Cell Syst 2021; 12:291-303. [PMID: 33887201 DOI: 10.1016/j.cels.2021.03.003] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/06/2020] [Revised: 01/19/2021] [Accepted: 03/17/2021] [Indexed: 12/16/2022]
Abstract
The fundamental mechanisms that control and regulate biological organisms exhibit a surprising level of complexity. Oscillators are perhaps the simplest motifs that produce time-varying dynamics and are ubiquitous in biological systems. It is also known that such biological oscillators interact with each other-for instance, circadian oscillators affect the cell cycle, and somitogenesis clock proteins in adjacent cells affect each other in developing embryos. Therefore, it is vital to understand the effects that can emerge from non-linear interaction between oscillations. Here, we show how oscillations typically arise in biology and take the reader on a tour through the great variety in dynamics that can emerge even from a single pair of coupled oscillators. We explain how chaotic dynamics can emerge and outline the methods of detecting this in experimental time traces. Finally, we discuss the potential role of such complex dynamical features in biological systems.
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Affiliation(s)
- Mathias L Heltberg
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark; Laboratoire de Physique Théorique, Ecole Normale Supérieure, 75 231 Paris Cedex 05, France
| | - Sandeep Krishna
- Simons Centre for the Study of Living Machines, National Centre for Biological Sciences TIFR, GKVK Campus, Bellary Road, Bangalore 560065, India
| | - Leo P Kadanoff
- The James Franck Institute, The University of Chicago, Chicago, IL 60637, USA
| | - Mogens H Jensen
- Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark; The James Franck Institute, The University of Chicago, Chicago, IL 60637, USA.
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34
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Stoliar P, Schneegans O, Rozenberg MJ. A Functional Spiking Neural Network of Ultra Compact Neurons. Front Neurosci 2021; 15:635098. [PMID: 33716656 PMCID: PMC7947689 DOI: 10.3389/fnins.2021.635098] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2020] [Accepted: 01/22/2021] [Indexed: 11/24/2022] Open
Abstract
We demonstrate that recently introduced ultra-compact neurons (UCN) with a minimal number of components can be interconnected to implement a functional spiking neural network. For concreteness we focus on the Jeffress model, which is a classic neuro-computational model proposed in the 40’s to explain the sound directionality detection by animals and humans. In addition, we introduce a long-axon neuron, whose architecture is inspired by the Hodgkin-Huxley axon delay-line and where the UCNs implement the nodes of Ranvier. We then interconnect two of those neurons to an output layer of UCNs, which detect coincidences between spikes propagating down the long-axons. This functional spiking neural neuron circuit with biological relevance is built from identical UCN blocks, which are simple enough to be made with off-the-shelf electronic components. Our work realizes a new, accessible and affordable physical model platform, where neuroscientists can construct arbitrary mid-size spiking neuronal networks in a lego-block like fashion that work in continuous time. This should enable them to address in a novel experimental manner fundamental questions about the nature of the neural code and to test predictions from mathematical models and algorithms of basic neurobiology research. The present work aims at opening a new experimental field of basic research in Spiking Neural Networks to a potentially large community, which is at the crossroads of neurobiology, dynamical systems, theoretical neuroscience, condensed matter physics, neuromorphic engineering, artificial intelligence, and complex systems.
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Affiliation(s)
- Pablo Stoliar
- National Institute of Advanced Industrial Science and Technology (AIST), Tsukuba, Japan
| | - Olivier Schneegans
- Université Paris-Saclay, Sorbonne Université, CentraleSupélec, CNRS, Laboratoire de Génie Électrique et Électronique de Paris, Gif-sur-Yvette, France
| | - Marcelo J Rozenberg
- Université Paris-Saclay, CNRS, Laboratoire de Physique des Solides, Orsay, France
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35
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Mao X, Li X, Ding W, Wang S, Zhou X, Qiao L. Dynamics of a multiplex neural network with delayed couplings. APPLIED MATHEMATICS AND MECHANICS 2021; 42:441-456. [PMID: 33551533 PMCID: PMC7852048 DOI: 10.1007/s10483-021-2709-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/06/2020] [Revised: 12/16/2020] [Indexed: 06/12/2023]
Abstract
Multiplex networks have drawn much attention since they have been observed in many systems, e.g., brain, transport, and social relationships. In this paper, the nonlinear dynamics of a multiplex network with three neural groups and delayed interactions is studied. The stability and bifurcation of the network equilibrium are discussed, and interesting neural activities of the network are explored. Based on the neuron circuit, transfer function circuit, and time delay circuit, a circuit platform of the network is constructed. It is shown that delayed couplings play crucial roles in the network dynamics, e.g., the enhancement and suppression of the stability, the patterns of the synchronization between networks, and the generation of complicated attractors and multi-stability coexistence.
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Affiliation(s)
- Xiaochen Mao
- Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 211100 China
| | - Xingyong Li
- Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 211100 China
| | - Weijie Ding
- Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 211100 China
| | - Song Wang
- Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 211100 China
| | - Xiangyu Zhou
- Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 211100 China
| | - Lei Qiao
- Department of Engineering Mechanics, College of Mechanics and Materials, Hohai University, Nanjing, 211100 China
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36
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Piccinini J, Ipiñna IP, Laufs H, Kringelbach M, Deco G, Sanz Perl Y, Tagliazucchi E. Noise-driven multistability vs deterministic chaos in phenomenological semi-empirical models of whole-brain activity. CHAOS (WOODBURY, N.Y.) 2021; 31:023127. [PMID: 33653038 DOI: 10.1063/5.0025543] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/17/2020] [Accepted: 01/29/2021] [Indexed: 06/12/2023]
Abstract
An outstanding open problem in neuroscience is to understand how neural systems are capable of producing and sustaining complex spatiotemporal dynamics. Computational models that combine local dynamics with in vivo measurements of anatomical and functional connectivity can be used to test potential mechanisms underlying this complexity. We compared two conceptually different mechanisms: noise-driven switching between equilibrium solutions (modeled by coupled Stuart-Landau oscillators) and deterministic chaos (modeled by coupled Rossler oscillators). We found that both models struggled to simultaneously reproduce multiple observables computed from the empirical data. This issue was especially manifested in the case of noise-driven dynamics close to a bifurcation, which imposed overly strong constraints on the optimal model parameters. In contrast, the chaotic model could produce complex behavior over a range of parameters, thus being capable of capturing multiple observables at the same time with good performance. Our observations support the view of the brain as a non-equilibrium system able to produce endogenous variability. We presented a simple model capable of jointly reproducing functional connectivity computed at different temporal scales. Besides adding to our conceptual understanding of brain complexity, our results inform and constrain the future development of biophysically realistic large-scale models.
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Affiliation(s)
- Juan Piccinini
- Buenos Aires Physics Institute and Physics Department, University of Buenos Aires, Buenos Aires 1428, Argentina
| | - Ignacio Perez Ipiñna
- Buenos Aires Physics Institute and Physics Department, University of Buenos Aires, Buenos Aires 1428, Argentina
| | - Helmut Laufs
- Neurology Department, University of Kiel, Kiel 24105, Germany
| | - Morten Kringelbach
- Department of Psychiatry, University of Oxford, Oxford OX3 7JX, United Kingdom
| | - Gustavo Deco
- Center for Brain and Cognition, Computational Neuroscience Group, Universitat Pompeu Fabra, Barcelona 08002, Spain
| | - Yonatan Sanz Perl
- Buenos Aires Physics Institute and Physics Department, University of Buenos Aires, Buenos Aires 1428, Argentina
| | - Enzo Tagliazucchi
- Buenos Aires Physics Institute and Physics Department, University of Buenos Aires, Buenos Aires 1428, Argentina
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37
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Sadeghijam M, Moossavi A, Akbari M. Does tinnitus lead to chaos? Braz J Otorhinolaryngol 2021; 87:125-126. [PMID: 33500207 PMCID: PMC9422581 DOI: 10.1016/j.bjorl.2020.11.022] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/20/2020] [Accepted: 11/30/2020] [Indexed: 10/31/2022] Open
Affiliation(s)
- Maryam Sadeghijam
- Iran University of Medical Science, School of Rehabilitation, Department of Audiology, Tehran, Iran
| | - Abdollah Moossavi
- Iran University of Medical Science, Department of Otolaryngology and Head and Neck Surgery, Tehran, Iran.
| | - Mahdi Akbari
- Iran University of Medical Science, School of Rehabilitation, Department of Audiology, Tehran, Iran
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38
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Saha S, Nagaraj N, Mathur A, Yedida R, H R S. Evolution of novel activation functions in neural network training for astronomy data: habitability classification of exoplanets. THE EUROPEAN PHYSICAL JOURNAL. SPECIAL TOPICS 2020; 229:2629-2738. [PMID: 33194093 PMCID: PMC7651829 DOI: 10.1140/epjst/e2020-000098-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/08/2020] [Accepted: 09/02/2020] [Indexed: 06/11/2023]
Abstract
Quantification of habitability is a complex task. Previous attempts at measuring habitability are well documented. Classification of exoplanets, on the other hand, is a different approach and depends on quality of training data available in habitable exoplanet catalogs. Classification is the task of predicting labels of newly discovered planets based on available class labels in the catalog. We present analytical exploration of novel activation functions as consequence of integration of several ideas leading to implementation and subsequent use in habitability classification of exoplanets. Neural networks, although a powerful engine in supervised methods, often require expensive tuning efforts for optimized performance. Habitability classes are hard to discriminate, especially when attributes used as hard markers of separation are removed from the data set. The solution is approached from the point of investigating analytical properties of the proposed activation functions. The theory of ordinary differential equations and fixed point are exploited to justify the "lack of tuning efforts" to achieve optimal performance compared to traditional activation functions. Additionally, the relationship between the proposed activation functions and the more popular ones is established through extensive analytical and empirical evidence. Finally, the activation functions have been implemented in plain vanilla feed-forward neural network to classify exoplanets. The mathematical exercise supplements the grand idea of classifying exoplanets, computing habitability scores/indices and automatic grouping of the exoplanets converging at some level.
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Affiliation(s)
- Snehanshu Saha
- CSIS and APPCAIR, BITS Pilani K K Birla, Goa Campus, Sancoale, India
| | - Nithin Nagaraj
- Consciousness Studies Programme, National Institute of Advanced Studies, Bengaluru, India
| | - Archana Mathur
- Nitte Meenakshi Institute of Technology, Bengaluru, India
| | | | - Sneha H R
- Nitte Meenakshi Institute of Technology, Bengaluru, India
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39
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Baghdadi G, Amiri M, Falotico E, Laschi C. Recurrence quantification analysis of EEG signals for tactile roughness discrimination. INT J MACH LEARN CYB 2020. [DOI: 10.1007/s13042-020-01224-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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40
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Inoue K, Nakajima K, Kuniyoshi Y. Designing spontaneous behavioral switching via chaotic itinerancy. SCIENCE ADVANCES 2020; 6:6/46/eabb3989. [PMID: 33177080 PMCID: PMC7673744 DOI: 10.1126/sciadv.abb3989] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/22/2020] [Accepted: 09/24/2020] [Indexed: 05/09/2023]
Abstract
Chaotic itinerancy is a frequently observed phenomenon in high-dimensional nonlinear dynamical systems and is characterized by itinerant transitions among multiple quasi-attractors. Several studies have pointed out that high-dimensional activity in animal brains can be observed to exhibit chaotic itinerancy, which is considered to play a critical role in the spontaneous behavior generation of animals. Thus, how to design desired chaotic itinerancy is a topic of great interest, particularly for neurorobotics researchers who wish to understand and implement autonomous behavioral controls. However, it is generally difficult to gain control over high-dimensional nonlinear dynamical systems. In this study, we propose a method for implementing chaotic itinerancy reproducibly in a high-dimensional chaotic neural network. We demonstrate that our method enables us to easily design both the trajectories of quasi-attractors and the transition rules among them simply by adjusting the limited number of system parameters and by using the intrinsic high-dimensional chaos.
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Affiliation(s)
- Katsuma Inoue
- Graduate School of Information Science and Technology, The University of Tokyo, Engineering Building 2, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
| | - Kohei Nakajima
- Graduate School of Information Science and Technology, The University of Tokyo, Engineering Building 2, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
| | - Yasuo Kuniyoshi
- Graduate School of Information Science and Technology, The University of Tokyo, Engineering Building 2, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan.
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41
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Abstract
In this paper, inertial neural networks are under investigation, that is, the second order differential equations. The recently introduced new type of motions, unpredictable oscillations, are considered for the models. The motions continue a line of periodic and almost periodic oscillations. The research is of very strong importance for neuroscience, since the existence of unpredictable solutions proves Poincaré chaos. Sufficient conditions have been determined for the existence, uniqueness, and exponential stability of unpredictable solutions. The results can significantly extend the role of oscillations for artificial neural networks exploitation, since they provide strong new theoretical and practical opportunities for implementation of methods of chaos extension, synchronization, stabilization, and control of periodic motions in various types of neural networks. Numerical simulations are presented to demonstrate the validity of the theoretical results.
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42
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Shah SAA, Zhang L, Bais A. Dynamical system based compact deep hybrid network for classification of Parkinson disease related EEG signals. Neural Netw 2020; 130:75-84. [DOI: 10.1016/j.neunet.2020.06.018] [Citation(s) in RCA: 24] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/10/2019] [Revised: 06/01/2020] [Accepted: 06/22/2020] [Indexed: 01/08/2023]
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43
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Dwyer DS. Genomic Chaos Begets Psychiatric Disorder. Complex Psychiatry 2020; 6:20-29. [PMID: 34883501 PMCID: PMC7673594 DOI: 10.1159/000507988] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/16/2019] [Accepted: 04/06/2020] [Indexed: 12/21/2022] Open
Abstract
The processes that created the primordial genome are inextricably linked to current day vulnerability to developing a psychiatric disorder as summarized in this review article. Chaos and dynamic forces including duplication, transposition, and recombination generated the protogenome. To survive early stages of genome evolution, self-organization emerged to curb chaos. Eventually, the human genome evolved through a delicate balance of chaos/instability and organization/stability. However, recombination coldspots, silencing of transposable elements, and other measures to limit chaos also led to retention of variants that increase risk for disease. Moreover, ongoing dynamics in the genome creates various new mutations that determine liability for psychiatric disorders. Homologous recombination, long-range gene regulation, and gene interactions were all guided by spooky action-at-a-distance, which increased variability in the system. A probabilistic system of life was required to deal with a changing environment. This ensured the generation of outliers in the population, which enhanced the probability that some members would survive unfavorable environmental impacts. Some of the outliers produced through this process in man are ill suited to cope with the complex demands of modern life. Genomic chaos and mental distress from the psychological challenges of modern living will inevitably converge to produce psychiatric disorders in man.
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Affiliation(s)
- Donard S. Dwyer
- Departments of Psychiatry and Behavioral Medicine and Pharmacology, Toxicology and Neuroscience, LSU Health Shreveport, Shreveport, Louisiana, USA
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44
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Takagi A, Furuta R, Saetia S, Yoshimura N, Koike Y, Minati L. Behavioral and physiological correlates of kinetically tracking a chaotic target. PLoS One 2020; 15:e0239471. [PMID: 32946493 PMCID: PMC7500904 DOI: 10.1371/journal.pone.0239471] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2020] [Accepted: 09/04/2020] [Indexed: 11/18/2022] Open
Abstract
Humans can innately track a moving target by anticipating its future position from a brief history of observations. While ballistic trajectories can be readily extrapolated, many natural and artificial systems are governed by more general nonlinear dynamics and, therefore, can produce highly irregular motion. Yet, relatively little is known regarding the behavioral and physiological underpinnings of prediction and tracking in the presence of chaos. Here, we investigated in lab settings whether participants could manually follow the orbit of a paradigmatic chaotic system, the Rössler equations, on the (x,y) plane under different settings of a control parameter, which determined the prominence of transients in the target position. Tracking accuracy was negatively related to the level of unpredictability and folding. Nevertheless, while participants initially reacted to the transients, they gradually learned to anticipate it. This was accompanied by a decrease in muscular co-contraction, alongside enhanced activity in the theta and beta EEG bands for the highest levels of chaoticity. Furthermore, greater phase synchronization of breathing was observed. Taken together, these findings point to the possible ability of the nervous system to implicitly learn topological regularities even in the context of highly irregular motion, reflecting in multiple observables at the physiological level.
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Affiliation(s)
- Atsushi Takagi
- NTT Communication Science Laboratories, Atsugi, Japan
- Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan
- Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency (JST), Kawaguchi, Japan
- * E-mail:
| | - Ryoga Furuta
- Department of Information and Communications Engineering, School of Engineering, Tokyo Institute of Technology, Yokohama, Japan
| | - Supat Saetia
- Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan
| | - Natsue Yoshimura
- Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan
- Precursory Research for Embryonic Science and Technology (PRESTO), Japan Science and Technology Agency (JST), Kawaguchi, Japan
| | - Yasuharu Koike
- Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan
| | - Ludovico Minati
- Institute of Innovative Research, Tokyo Institute of Technology, Yokohama, Japan
- CIMeC, Center for Mind/Brain Sciences, University of Trento, Trento, Italy
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45
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A Review of the Serrated-Flow Phenomenon and Its Role in the Deformation Behavior of High-Entropy Alloys. METALS 2020. [DOI: 10.3390/met10081101] [Citation(s) in RCA: 53] [Impact Index Per Article: 13.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
High-entropy alloys (HEAs) are a novel class of alloys that have many desirable properties. The serrated flow that occurs in high-entropy alloys during mechanical deformation is an important phenomenon since it can lead to significant changes in the microstructure of the alloy. In this article, we review the recent findings on the serration behavior in a variety of high-entropy alloys. Relationships among the serrated flow behavior, composition, microstructure, and testing condition are explored. Importantly, the mechanical-testing type (compression/tension), testing temperature, applied strain rate, and serration type for certain high-entropy alloys are summarized. The literature reveals that the serrated flow can be affected by experimental conditions such as the strain rate and test temperature. Furthermore, this type of phenomenon has been successfully modeled and analyzed, using several different types of analytical methods, including the mean-field theory formalism and the complexity-analysis technique. Importantly, the results of the analyses show that the serrated flow in HEAs consists of complex dynamical behavior. It is anticipated that this review will provide some useful and clarifying information regarding the serrated-flow mechanisms in this material system. Finally, suggestions for future research directions in this field are proposed, such as the effects of irradiation, additives (such as C and Al), the presence of nanoparticles, and twinning on the serrated flow behavior in HEAs.
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46
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Barrio R, Ibáñez S, Pérez L. Homoclinic organization in the Hindmarsh-Rose model: A three parameter study. CHAOS (WOODBURY, N.Y.) 2020; 30:053132. [PMID: 32491901 DOI: 10.1063/1.5138919] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/16/2019] [Accepted: 04/24/2020] [Indexed: 06/11/2023]
Abstract
Bursting phenomena are found in a wide variety of fast-slow systems. In this article, we consider the Hindmarsh-Rose neuron model, where, as it is known in the literature, there are homoclinic bifurcations involved in the bursting dynamics. However, the global homoclinic structure is far from being fully understood. Working in a three-parameter space, the results of our numerical analysis show a complex atlas of bifurcations, which extends from the singular limit to regions where a fast-slow perspective no longer applies. Based on this information, we propose a global theoretical description. Surfaces of codimension-one homoclinic bifurcations are exponentially close to each other in the fast-slow regime. Remarkably, explained by the specific properties of these surfaces, we show how the Hindmarsh-Rose model exhibits isolas of homoclinic bifurcations when appropriate two-dimensional slices are considered in the three-parameter space. On the other hand, these homoclinic bifurcation surfaces contain curves corresponding to parameter values where additional degeneracies are exhibited. These codimension-two bifurcation curves organize the bifurcations associated with the spike-adding process and they behave like the "spines-of-a-book," gathering "pages" of bifurcations of periodic orbits. Depending on how the parameter space is explored, homoclinic phenomena may be absent or far away, but their organizing role in the bursting dynamics is beyond doubt, since the involved bifurcations are generated in them. This is shown in the global analysis and in the proposed theoretical scheme.
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Affiliation(s)
- Roberto Barrio
- Departamento de Matemática Aplicada and IUMA, University of Zaragoza, E-50009 Zaragoza, Spain
| | - Santiago Ibáñez
- Departamento de Matemáticas, University of Oviedo, E-33007 Oviedo, Spain
| | - Lucía Pérez
- Departamento de Matemáticas, University of Oviedo, E-33007 Oviedo, Spain
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Leng Y, Yu D, Hu Y, Yu SS, Ye Z. Dynamic behaviors of hyperbolic-type memristor-based Hopfield neural network considering synaptic crosstalk. CHAOS (WOODBURY, N.Y.) 2020; 30:033108. [PMID: 32237757 DOI: 10.1063/5.0002076] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Accepted: 02/06/2020] [Indexed: 06/11/2023]
Abstract
Crosstalk phenomena taking place between synapses can influence signal transmission and, in some cases, brain functions. It is thus important to discover the dynamic behaviors of the neural network infected by synaptic crosstalk. To achieve this, in this paper, a new circuit is structured to emulate the Coupled Hyperbolic Memristors, which is then utilized to simulate the synaptic crosstalk of a Hopfield Neural Network (HNN). Thereafter, the HNN's multi-stability, asymmetry attractors, and anti-monotonicity are observed with various crosstalk strengths. The dynamic behaviors of the HNN are presented using bifurcation diagrams, dynamic maps, and Lyapunov exponent spectrums, considering different levels of crosstalk strengths. Simulation results also reveal that different crosstalk strengths can lead to wide-ranging nonlinear behaviors in the HNN systems.
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Affiliation(s)
- Yang Leng
- School of Electrical and Power Engineering, China University of Mining and Technology, No. 1 Daxue Road, Xuzhou, Jiangsu 221116, China
| | - Dongsheng Yu
- School of Electrical and Power Engineering, China University of Mining and Technology, No. 1 Daxue Road, Xuzhou, Jiangsu 221116, China
| | - Yihua Hu
- School of Electrical and Power Engineering, China University of Mining and Technology, No. 1 Daxue Road, Xuzhou, Jiangsu 221116, China
| | - Samson Shenglong Yu
- School of Engineering, Deakin University, 75 Pigdons Road, Waurn Ponds, Victoria 3216, Australia
| | - Zongbin Ye
- School of Electrical and Power Engineering, China University of Mining and Technology, No. 1 Daxue Road, Xuzhou, Jiangsu 221116, China
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A contribution to neuromorphic engineering: neuromodulation implemented through photochromic compounds maintained out of equilibrium by UV–visible radiation. RENDICONTI LINCEI. SCIENZE FISICHE E NATURALI 2020. [DOI: 10.1007/s12210-020-00869-y] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
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49
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Toker D, Sommer FT, D’Esposito M. A simple method for detecting chaos in nature. Commun Biol 2020; 3:11. [PMID: 31909203 PMCID: PMC6941982 DOI: 10.1038/s42003-019-0715-9] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2019] [Accepted: 11/26/2019] [Indexed: 11/18/2022] Open
Abstract
Chaos, or exponential sensitivity to small perturbations, appears everywhere in nature. Moreover, chaos is predicted to play diverse functional roles in living systems. A method for detecting chaos from empirical measurements should therefore be a key component of the biologist's toolkit. But, classic chaos-detection tools are highly sensitive to measurement noise and break down for common edge cases, making it difficult to detect chaos in domains, like biology, where measurements are noisy. However, newer tools promise to overcome these limitations. Here, we combine several such tools into an automated processing pipeline, and show that our pipeline can detect the presence (or absence) of chaos in noisy recordings, even for difficult edge cases. As a first-pass application of our pipeline, we show that heart rate variability is not chaotic as some have proposed, and instead reflects a stochastic process in both health and disease. Our tool is easy-to-use and freely available.
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Affiliation(s)
- Daniel Toker
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA USA
| | - Friedrich T. Sommer
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA USA
| | - Mark D’Esposito
- Helen Wills Neuroscience Institute, University of California, Berkeley, CA USA
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International Federation of Clinical Neurophysiology (IFCN) – EEG research workgroup: Recommendations on frequency and topographic analysis of resting state EEG rhythms. Part 1: Applications in clinical research studies. Clin Neurophysiol 2020; 131:285-307. [DOI: 10.1016/j.clinph.2019.06.234] [Citation(s) in RCA: 94] [Impact Index Per Article: 23.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/31/2017] [Revised: 05/17/2019] [Accepted: 06/02/2019] [Indexed: 01/22/2023]
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