1
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Huang C, Mo S, Cao J. Detections of bifurcation in a fractional-order Cohen-Grossberg neural network with multiple delays. Cogn Neurodyn 2024; 18:1379-1396. [PMID: 38826673 PMCID: PMC11143155 DOI: 10.1007/s11571-023-09934-2] [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: 12/10/2021] [Revised: 12/25/2022] [Accepted: 01/24/2023] [Indexed: 03/06/2023] Open
Abstract
The dynamics of integer-order Cohen-Grossberg neural networks with time delays has lately drawn tremendous attention. It reveals that fractional calculus plays a crucial role on influencing the dynamical behaviors of neural networks (NNs). This paper deals with the problem of the stability and bifurcation of fractional-order Cohen-Grossberg neural networks (FOCGNNs) with two different leakage delay and communication delay. The bifurcation results with regard to leakage delay are firstly gained. Then, communication delay is viewed as a bifurcation parameter to detect the critical values of bifurcations for the addressed FOCGNN, and the communication delay induced-bifurcation conditions are procured. We further discover that fractional orders can enlarge (reduce) stability regions of the addressed FOCGNN. Furthermore, we discover that, for the same system parameters, the convergence time to the equilibrium point of FONN is shorter (longer) than that of integer-order NNs. In this paper, the present methodology to handle the characteristic equation with triple transcendental terms in delayed FOCGNNs is concise, neoteric and flexible in contrast with the prior mechanisms owing to skillfully keeping away from the intricate classified discussions. Eventually, the developed analytic results are nicely showcased by the simulation examples.
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Affiliation(s)
- Chengdai Huang
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000 China
| | - Shansong Mo
- School of Mathematics and Statistics, Xinyang Normal University, Xinyang, 464000 China
| | - Jinde Cao
- School of Mathematics, Southeast University, Nanjing, 210096 China
- Yonsei Frontier Lab, Yonsei University, Seoul, 03722 South Korea
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2
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Bao B, Hu J, Bao H, Xu Q, Chen M. Memristor-coupled dual-neuron mapping model: initials-induced coexisting firing patterns and synchronization activities. Cogn Neurodyn 2024; 18:539-555. [PMID: 38699613 PMCID: PMC11061084 DOI: 10.1007/s11571-023-10006-8] [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: 02/20/2023] [Revised: 07/25/2023] [Accepted: 08/24/2023] [Indexed: 05/05/2024] Open
Abstract
Synaptic plasticity makes memristors particularly suitable for simulating the connection synapses between neurons that describe magnetic induction coupling. By applying a memristor to the synaptic coupling between two map-based neuron models, a memristor-coupled dual-neuron mapping (MCDN) model is proposed in this article. The MCDN model has a line fixed point set associated with the memristor initial state, which is always unstable for the model parameters and memristor initial state of interest. Complex spiking/bursting firing patterns and their transitions are disclosed using some dynamical analysis means. The numerical results show that these spiking/bursting firings are significantly relied on the memristor initial state, demonstrating the coexistence of firing patterns. Moreover, the initial effects of complete synchronization are explored for the homogeneous MCDN model, and it is clarified that in addition to being related to the coupling strength, the synchronization activities are extremely dependent on the initial states of the memristor and neurons. Finally, these numerical results are confirmed by the FPGA-based hardware experiments.
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Affiliation(s)
- Bocheng Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Jingting Hu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Han Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Quan Xu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Mo Chen
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
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3
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Xu Q, Wang K, Shan Y, Wu H, Chen M, Wang N. Dynamical effects of memristive electromagnetic induction on a 2D Wilson neuron model. Cogn Neurodyn 2024; 18:645-657. [PMID: 38699611 PMCID: PMC11061083 DOI: 10.1007/s11571-023-10014-8] [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: 08/03/2023] [Revised: 09/04/2023] [Accepted: 09/16/2023] [Indexed: 05/05/2024] Open
Abstract
Electromagnetic induction plays a crucial impact on the firing activity of biological neurons, since it exists along with the mutual effect between membrane potential and ions transport. Flux-controlled memristor is an available candidate in characterizing the electromagnetic induction effect. Different from the previously reported literature, a non-ideal flux-controlled memristor with cosine mem-conductance function is employed to determine the periodic magnetization and leakage flux processes in neurons. Thereafter, a three-dimensional (3D) memristive Wilson (m-Wilson) neuron model is constructed under the consideration of this kind of electromagnetic induction. Numerical simulations are performed by multiple numerical tools, which demonstrate that the 3D m-Wilson neuron model can generate abundant firing activities. Interestingly, coexisting firing activities, antimonotonicity, and firing frequency regulation are discovered under special parameter settings. Furthermore, a PCB-based analog circuit is designed and hardware measurements are executed to verify the numerical simulations. These explorations in numerical and hardware surveys might provide insights to regulate the firing activities by appropriate electromagnetic induction.
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Affiliation(s)
- Quan Xu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Kai Wang
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Yufan Shan
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Huagan Wu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Mo Chen
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
| | - Ning Wang
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213159 People’s Republic of China
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4
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Bao H, Yu X, Xu Q, Wu H, Bao B. Three-dimensional memristive Morris-Lecar model with magnetic induction effects and its FPGA implementation. Cogn Neurodyn 2023; 17:1079-1092. [PMID: 37522038 PMCID: PMC10374513 DOI: 10.1007/s11571-022-09871-6] [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: 05/20/2022] [Revised: 07/14/2022] [Accepted: 08/05/2022] [Indexed: 11/03/2022] Open
Abstract
To characterize the magnetic induction flow induced by neuron membrane potential, a three-dimensional (3D) memristive Morris-Lecar (ML) neuron model is proposed in this paper. It is achieved using a memristor induction current to replace the slow modulation current in the existing 3D ML neuron model with fast-slow structure. The magnetic induction effects on firing activities are explained by the spiking/bursting firings with period-adding bifurcation and periodic/chaotic spiking-bursting patterns, and the bifurcation mechanisms of the bursting patterns are elaborated using the fast-slow analysis method to create two bifurcation sets. In particular, the 3D memristive ML model can also exhibit the homogeneous coexisting bursting patterns when switching the memristor initial states, which are effectively illustrated by the theoretical analysis and numerical simulations. Finally, a digitally FPGA-based hardware platform is developed for the 3D memristive ML model and the experimentally measured results well verify the numerical ones.
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Affiliation(s)
- Han Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 People’s Republic of China
| | - Xihong Yu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 People’s Republic of China
| | - Quan Xu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 People’s Republic of China
| | - Huagan Wu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 People’s Republic of China
| | - Bocheng Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 People’s Republic of China
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5
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Xu C, Liao M, Wang C, Sun J, Lin H. Memristive competitive hopfield neural network for image segmentation application. Cogn Neurodyn 2023; 17:1061-1077. [PMID: 37522050 PMCID: PMC10374519 DOI: 10.1007/s11571-022-09891-2] [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: 11/04/2021] [Revised: 09/06/2022] [Accepted: 09/18/2022] [Indexed: 11/30/2022] Open
Abstract
Image segmentation implementation provides simplified and effective feature information of image. Neural network algorithms have made significant progress in the application of image segmentation task. However, few studies focus on the implementation of hardware circuits with high-efficiency analog calculations and parallel operations for image segmentation problem. In this paper, a memristor-based competitive Hopfield neural network circuit is proposed to deal with the image segmentation problem. In this circuit, the memristive cross array is applied to store synaptic weights and perform matrix operations. The competition module based on the Winner-take-all mechanism is composed of the competition neurons and the competition control circuit, which simplifies the energy function of the Hopfield neural network and realizes the output function. Operational amplifiers and ABM modules are used to integrate operations and process external input information, respectively. Based on these designs, the circuit can automatically implement iteration and update of data. A series of PSPICE simulations are designed to verify the image segmentation capability of this circuit. Comparative experimental results and analysis show that this circuit has effective improvements both in processing speed and segmentation accuracy compared with other methods. Moreover, the proposed circuit shows good robustness to noise and memristive variation.
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Affiliation(s)
- Cong Xu
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, 410082 China
| | - Meiling Liao
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, 410082 China
| | - Chunhua Wang
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, 410082 China
| | - Jingru Sun
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, 410082 China
| | - Hairong Lin
- College of Computer Science and Electronic Engineering, Hunan University, Changsha, 410082 China
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Xu Q, Liu T, Ding S, Bao H, Li Z, Chen B. Extreme multistability and phase synchronization in a heterogeneous bi-neuron Rulkov network with memristive electromagnetic induction. Cogn Neurodyn 2023; 17:755-766. [PMID: 37265650 PMCID: PMC10229522 DOI: 10.1007/s11571-022-09866-3] [Citation(s) in RCA: 7] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/18/2022] [Revised: 07/13/2022] [Accepted: 07/18/2022] [Indexed: 11/03/2022] Open
Abstract
Memristive electromagnetic induction effect has been widely explored in bi-neuron network with homogeneous neurons, but rarely in bi-neuron network with heterogeneous ones. This paper builds a bi-neuron network by coupling heterogeneous Rulkov neurons with memristor and investigates the memristive electromagnetic induction effect. Theoretical analysis discloses that the bi-neuron network possesses a line equilibrium state and its stability depends on the memristor coupling strength and initial condition. That is, the stability of the line equilibrium state has a transition between unstable saddle-focus and stable node-focus via Hopf bifurcation. By employing parameters located in the stable node-focus region, dynamical behaviors related to the memristor coupling strength and initial conditions are revealed by Julia- and MATLAB-based multiple numerical tools. Numerical results demonstrate that the proposed heterogeneous bi-neuron Rulkov network can generate point attractor, period, chaos, chaos crisis, and period-doubling bifurcation. Note that extreme multistability are disclosed with respect to initial conditions of memristor and gated ion concentration. Coexisting infinitely multiple firing patterns of periodic firing patterns with different periodicities and chaotic firing patterns for different memristor initial conditions are demonstrated by phase portrait and time-domain waveform. Besides, the phase synchronization related to the memristor coupling strength and its initial condition is explored, which suggests that the two heterogeneous neurons become phase synchronization with large memristor coupling strength and initial condition. This also reflects that the plasticity of memristor synapse enables adaptive regulation in keeping energy balance between the neurons. What's more, MCU-based hardware experiments are executed to further confirm the numerical simulations.
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Affiliation(s)
- Quan Xu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Tong Liu
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Shoukui Ding
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Han Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Ze Li
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
| | - Bei Chen
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou, 213164 China
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7
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Variations of the spontaneous electrical activities of the neuronal networks imposed by the exposure of electromagnetic radiations using computational map-based modeling. J Comput Neurosci 2023; 51:187-200. [PMID: 36539556 DOI: 10.1007/s10827-022-00842-8] [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: 08/03/2022] [Revised: 12/01/2022] [Accepted: 12/04/2022] [Indexed: 01/15/2023]
Abstract
The interaction between neurons in a neuronal network develops spontaneous electrical activities. But the effects of electromagnetic radiation on these activities have not yet been well explored. In this study, a ring of three coupled 1-dimensional Rulkov neurons and the generated electromagnetic field (EMF) are considered to investigate how the spontaneous activities might change regarding the EMF exposure. By employing the bifurcation analysis and time series, a comprehensive view of neuronal behavioral changes due to electromagnetic inductions is provided. The main findings of this study are as follows: 1) When a neuronal network is showing a spontaneous chaotic firing manner (without any external stimuli), a generated magnetic field inhibits this type of behavior. In fact, EMF completely eliminated the chaotic intrinsic behaviors of the neuronal loop. 2) When the network is exhibiting regular period-3 spiking patterns, the generated magnetic field changes its firing pattern to chaotic spiking, which is similar to epileptic seizures. 3) With weak synaptic connections, electromagnetic radiation inhibits and suppresses neuronal activities. 4) If the external magnetic flux has a high amplitude, it can change the shape of the induction current according to its shape 5) when there are weak synaptic connections in the network, a high-frequency external magnetic flux engenders high-frequency fluctuations in the membrane voltages. On the whole, electromagnetic radiation changes the pattern of the spontaneous activities of neuronal networks in the brain according to synaptic strengths and initial states of the neurons.
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8
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Wang J, Shen J. Turing instability mechanism of short-memory formation in multilayer FitzHugh-Nagumo network. Front Psychiatry 2023; 14:1083015. [PMID: 37051165 PMCID: PMC10083418 DOI: 10.3389/fpsyt.2023.1083015] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 10/28/2022] [Accepted: 02/14/2023] [Indexed: 04/14/2023] Open
Abstract
Introduction The study of brain function has been favored by scientists, but the mechanism of short-term memory formation has yet to be precise. Research problem Since the formation of short-term memories depends on neuronal activity, we try to explain the mechanism from the neuron level in this paper. Research contents and methods Due to the modular structures of the brain, we analyze the pattern properties of the FitzHugh-Nagumo model (FHN) on a multilayer network (coupled by a random network). The conditions of short-term memory formation in the multilayer FHN model are obtained. Then the time delay is introduced to more closely match patterns of brain activity. The properties of periodic solutions are obtained by the central manifold theorem. Conclusion When the diffusion coeffcient, noise intensity np, and network connection probability p reach a specific range, the brain forms a relatively vague memory. It is found that network and time delay can induce complex cluster dynamics. And the synchrony increases with the increase of p. That is, short-term memory becomes clearer.
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Affiliation(s)
- Junjie Wang
- School of Mathematics and Statistics, Zhengzhou University, Zhengzhou, China
| | - Jianwei Shen
- School of Mathematics and Statistics, North China University of Water Resources and Electric Power, Zhengzhou, China
- *Correspondence: Jianwei Shen
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9
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Bao H, Zhang J, Wang N, Kuznetsov NV, Bao BC. Adaptive synapse-based neuron model with heterogeneous multistability and riddled basins. CHAOS (WOODBURY, N.Y.) 2022; 32:123101. [PMID: 36587361 DOI: 10.1063/5.0125611] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/13/2022] [Accepted: 11/07/2022] [Indexed: 06/17/2023]
Abstract
Biological neurons can exhibit complex coexisting multiple firing patterns dependent on initial conditions. To this end, this paper presents a novel adaptive synapse-based neuron (ASN) model with sine activation function. The ASN model has time-varying equilibria with the variation of externally applied current and its equilibrium stability involves transitions between stable and unstable points through fold and Hopf bifurcations, resulting in complex distributions of attractive regions with heterogeneous multi-stability. Globally coexisting heterogeneous behaviors are studied by bifurcation diagram, phase portrait, dynamical distribution, and basin of attraction. The results show that the number of coexisting heterogeneous attractors can be up to 12, but for a simple neuron model, such a large number of coexisting heterogeneous attractors has not been reported in the relevant literature. Most interestingly, the ASN model also has riddled-like complex basins of attraction and four illustrative examples are depicted by the phase portraits with small changes of the initial conditions. Besides, the ASN model is implemented using a simple microcontroller platform, and various heterogeneous coexisting attractors are acquired experimentally to validate the numerical results.
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Affiliation(s)
- H Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
| | - J Zhang
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
| | - N Wang
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
| | - N V Kuznetsov
- Faculty of Mathematics and Mechanics, St. Petersburg State University, Peterhof, St. Petersburg 198504, Russia
| | - B C Bao
- School of Microelectronics and Control Engineering, Changzhou University, Changzhou 213164, China
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Bönsel F, Krauss P, Metzner C, Yamakou ME. Control of noise-induced coherent oscillations in three-neuron motifs. Cogn Neurodyn 2021; 16:941-960. [PMID: 35847543 PMCID: PMC9279551 DOI: 10.1007/s11571-021-09770-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2021] [Revised: 10/27/2021] [Accepted: 11/27/2021] [Indexed: 12/04/2022] Open
Abstract
The phenomenon of self-induced stochastic resonance (SISR) requires a nontrivial scaling limit between the deterministic and the stochastic timescales of an excitable system, leading to the emergence of coherent oscillations which are absent without noise. In this paper, we numerically investigate SISR and its control in single neurons and three-neuron motifs made up of the Morris–Lecar model. In single neurons, we compare the effects of electrical and chemical autapses on the degree of coherence of the oscillations due to SISR. In the motifs, we compare the effects of altering the synaptic time-delayed couplings and the topologies on the degree of SISR. Finally, we provide two enhancement strategies for a particularly poor degree of SISR in motifs with chemical synapses: (1) we show that a poor SISR can be significantly enhanced by attaching an electrical or an excitatory chemical autapse on one of the neurons, and (2) we show that by multiplexing the motif with a poor SISR to another motif (with a high SISR in isolation), the degree of SISR in the former motif can be significantly enhanced. We show that the efficiency of these enhancement strategies depends on the topology of the motifs and the nature of synaptic time-delayed couplings mediating the multiplexing connections.
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Affiliation(s)
- Florian Bönsel
- Chair for Dynamics, Control and Numerics, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
- Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestr. 91, 91052 Erlangen, Germany
| | - Patrick Krauss
- Neuroscience Lab, University Hospital Erlangen, Friedrich-Alexander-Universität Erlangen-Nürnberg, Waldstr. 1, 91054 Erlangen, Germany
| | - Claus Metzner
- Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg, Henkestr. 91, 91052 Erlangen, Germany
| | - Marius E. Yamakou
- Chair for Dynamics, Control and Numerics, Department of Data Science, Friedrich-Alexander-Universität Erlangen-Nürnberg, Cauerstr. 11, 91058 Erlangen, Germany
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Njitacke ZT, Koumetio BN, Ramakrishnan B, Leutcho GD, Fozin TF, Tsafack N, Rajagopal K, Kengne J. Hamiltonian energy and coexistence of hidden firing patterns from bidirectional coupling between two different neurons. Cogn Neurodyn 2021; 16:899-916. [PMID: 35847537 PMCID: PMC9279548 DOI: 10.1007/s11571-021-09747-1] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2021] [Revised: 10/27/2021] [Accepted: 11/03/2021] [Indexed: 11/30/2022] Open
Abstract
In this paper, bidirectional-coupled neurons through an asymmetric electrical synapse are investigated. These coupled neurons involve 2D Hindmarsh–Rose (HR) and 2D FitzHugh–Nagumo (FN) neurons. The equilibria of the coupled neurons model are investigated, and their stabilities have revealed that, for some values of the electrical synaptic weight, the model under consideration can display either self-excited or hidden firing patterns. In addition, the hidden coexistence of chaotic bursting with periodic spiking, chaotic spiking with period spiking, chaotic bursting with a resting pattern, and the coexistence of chaotic spiking with a resting pattern are also found for some sets of electrical synaptic coupling. For all the investigated phenomena, the Hamiltonian energy of the model is computed. It enables the estimation of the amount of energy released during the transition between the various electrical activities. Pspice simulations are carried out based on the analog circuit of the coupled neurons to support our numerical results. Finally, an STM32F407ZE microcontroller development board is exploited for the digital implementation of the proposed coupled neurons model.
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Affiliation(s)
- Zeric Tabekoueng Njitacke
- Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon
- Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
- Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, Lodz, Poland
| | - Bernard Nzoko Koumetio
- Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
- Research Unit of Condensed Matter, Department of Physics, Faculty of Sciences, Electronics and Signal Processing (UR-MACETS), University of Dschang, P.O. Box 67, Dschang, Cameroon
| | | | - Gervais Dolvis Leutcho
- Research Unit of Condensed Matter, Department of Physics, Faculty of Sciences, Electronics and Signal Processing (UR-MACETS), University of Dschang, P.O. Box 67, Dschang, Cameroon
- Department of Electrical Engineering, École de Technologie Supérieure (ÉTS), Montréal, Québec H3C1K3 Canada
| | - Theophile Fonzin Fozin
- Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P.O. Box 63, Buea, Cameroon
| | - Nestor Tsafack
- Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
- Research Unit of Condensed Matter, Department of Physics, Faculty of Sciences, Electronics and Signal Processing (UR-MACETS), University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - Kartikeyan Rajagopal
- Center for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamil Nadu India
| | - Jacques Kengne
- Research Unit of Automation and Applied Computer (URAIA), Electrical Engineering Department of IUT-FV, University of Dschang, P.O. Box 134, Bandjoun, Cameroon
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12
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Ding D, Jiang L, Hu Y, Yang Z, Li Q, Zhang Z, Wu Q. Hidden coexisting firings in fractional-order hyperchaotic memristor-coupled HR neural network with two heterogeneous neurons and its applications. CHAOS (WOODBURY, N.Y.) 2021; 31:083107. [PMID: 34470251 DOI: 10.1063/5.0053929] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/13/2021] [Accepted: 07/09/2021] [Indexed: 06/13/2023]
Abstract
The firing patterns of each bursting neuron are different because of the heterogeneity, which may be derived from the different parameters or external drives of the same kind of neurons, or even neurons with different functions. In this paper, the different electromagnetic effects produced by two fractional-order memristive (FOM) Hindmarsh-Rose (HR) neuron models are selected for characterizing different firing patterns of heterogeneous neurons. Meanwhile, a fractional-order memristor-coupled heterogeneous memristive HR neural network is constructed via coupling these two heterogeneous FOM HR neuron models, which has not been reported in the adjacent neuron models with memristor coupling. With the study of initial-depending bifurcation behaviors of the system, it is found that the system exhibits abundant hidden firing patterns, such as periods with different topologies, quasiperiodic firings, chaos with different topologies, and even hyperchaotic firings. Particularly, the hidden hyperchaotic firings are perfectly detected by two-dimensional Lyapunov stability graphs in the two-parameter space. Meanwhile, the hidden coexisting firing patterns of the system are excited from two scattered attraction domains, which can be confirmed from the local attraction basins. Furthermore, the color image encryption based on the system and the DNA approach owns great keyspace and a good encryption effect. Finally, the digital implementations based on Advanced RISC Machine are in good coincidence with numerical simulations.
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Affiliation(s)
- Dawei Ding
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Li Jiang
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Yongbing Hu
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Zongli Yang
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Qian Li
- School of Electronics and Information Engineering, Anhui University, Hefei 230601, China
| | - Zhixin Zhang
- School of Mathematics Sciences, Anhui University, Hefei 230601, China
| | - Qiujie Wu
- School of Internet, Anhui University, Hefei 230601, China
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13
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Ye W. Dynamics of a Large-Scale Spiking Neural Network with Quadratic Integrate-and-Fire Neurons. Neural Plast 2021; 2021:6623926. [PMID: 33679968 PMCID: PMC7925051 DOI: 10.1155/2021/6623926] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/04/2020] [Revised: 01/18/2021] [Accepted: 02/05/2021] [Indexed: 11/17/2022] Open
Abstract
Since the high dimension and complexity of the large-scale spiking neural network, it is difficult to research the network dynamics. In recent decades, the mean-field approximation has been a useful method to reduce the dimension of the network. In this study, we construct a large-scale spiking neural network with quadratic integrate-and-fire neurons and reduce it to a mean-field model to research the network dynamics. We find that the activity of the mean-field model is consistent with the network activity. Based on this agreement, a two-parameter bifurcation analysis is performed on the mean-field model to understand the network dynamics. The bifurcation scenario indicates that the network model has the quiescence state, the steady state with a relatively high firing rate, and the synchronization state which correspond to the stable node, stable focus, and stable limit cycle of the system, respectively. There exist several stable limit cycles with different periods, so we can observe the synchronization states with different periods. Additionally, the model shows bistability in some regions of the bifurcation diagram which suggests that two different activities coexist in the network. The mechanisms that how these states switch are also indicated by the bifurcation curves.
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Affiliation(s)
- Weijie Ye
- School of Statistics and Mathematics, Guangdong University of Finance and Economics, Guangzhou 510320, China
- Big data and Educational Statistics Application Laboratory, Guangdong University of Finance and Economics, Guangzhou 510320, China
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Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption. Neural Comput Appl 2020. [DOI: 10.1007/s00521-020-05451-z 10.1007/s00521-020-05451-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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15
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Njitacke ZT, Isaac SD, Nestor T, Kengne J. Window of multistability and its control in a simple 3D Hopfield neural network: application to biomedical image encryption. Neural Comput Appl 2020; 33:6733-6752. [PMID: 33169051 PMCID: PMC7641660 DOI: 10.1007/s00521-020-05451-z] [Citation(s) in RCA: 33] [Impact Index Per Article: 8.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/19/2020] [Accepted: 10/14/2020] [Indexed: 11/03/2022]
Abstract
In this contribution, the problem of multistability control in a simple model of 3D HNNs as well as its application to biomedical image encryption is addressed. The space magnetization is justified by the coexistence of up to six disconnected attractors including both chaotic and periodic. The linear augmentation method is successfully applied to control the multistable HNNs into a monostable network. The control of the coexisting four attractors including a pair of chaotic attractors and a pair of periodic attractors is made through three crises that enable the chaotic attractors to be metamorphosed in a monostable periodic attractor. Also, the control of six coexisting attractors (with two pairs of chaotic attractors and a pair of periodic one) is made through five crises enabling all the chaotic attractors to be metamorphosed in a monostable periodic attractor. Note that this controlled HNN is obtained for higher values of the coupling strength. These interesting results are obtained using nonlinear analysis tools such as the phase portraits, bifurcations diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The obtained results have been perfectly supported using the PSPICE simulation environment. Finally, a simple encryption scheme is designed jointly using the sequences of the proposed HNNs and the sequences of real/imaginary values of the Julia fractals set. The obtained cryptosystem is validated using some well-known metrics. The proposed method achieved entropy of 7.9992, NPCR of 99.6299, and encryption time of 0.21 for the 256*256 sample 1 image.
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Affiliation(s)
- Zeric Tabekoueng Njitacke
- Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon.,Unité de Recherche D'Automatique et Informatique Appliquée (URAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon
| | - Sami Doubla Isaac
- Unité de Recherche D'Automatique et Informatique Appliquée (URAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon.,Unité de Recherche de Matière Condensée, d'Electronique et de Traitement du Signal (URAMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - Tsafack Nestor
- Unité de Recherche D'Automatique et Informatique Appliquée (URAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon.,Unité de Recherche de Matière Condensée, d'Electronique et de Traitement du Signal (URAMACETS), Department of Physics, University of Dschang, P.O. Box 67, Dschang, Cameroon
| | - Jacques Kengne
- Unité de Recherche D'Automatique et Informatique Appliquée (URAIA), Department of Electrical Engineering, IUT-FV Bandjoun, University of Dschang, Dschang, Cameroon
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