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Sriram S, Mirzaei S, Mehrabbeik M, Rajagopal K, Rostami M, Jafari S. The influence of synaptic pathways on the synchronization patterns of regularly structured mChialvo map network. J Theor Biol 2023; 572:111591. [PMID: 37543300 DOI: 10.1016/j.jtbi.2023.111591] [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: 06/13/2023] [Revised: 07/26/2023] [Accepted: 07/28/2023] [Indexed: 08/07/2023]
Abstract
Synchronization of interconnecting units is one of the hottest topics many researchers are interested in. In addition, this emerging phenomenon is responsible for many biological processes, and thus, the synchronization of interacting neurons is an important field of study in neuroscience. Employing the memristive Chialvo (mChialvo) neuron map, this paper investigates the effect of electrical, inner-linking, chemical, and hybrid coupling functions on the synchronization state of a neuronal network with regular structure. Master stability function (MSF) analysis is performed to obtain the necessary conditions for synchronizing the built networks. Afterward, the MSF-based results are confirmed by calculating the synchronization error. Besides, the dynamics of the synchronous neurons are discussed based on the bifurcation analysis. Our results suggest that, compared to the electrical and inner-linking functions, chemical synapses facilitate mChialvo neurons' synchronization since the neurons can achieve synchrony with a negligible chemical coupling strength. Further studies reveal that based on the active synapses, coupled mChialvo neurons can reach cluster synchronization, chimera state, sine-like synchronization, phase synchronization, and cluster phase synchronization.
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Affiliation(s)
- Sridevi Sriram
- Centre for Computational Modelling, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Simin Mirzaei
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Mahtab Mehrabbeik
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, Tamil Nadu, India
| | - Mehdi Rostami
- Department of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran; Health Technology Research Institute, Amirkabir University of Technology (Tehran Polytechnic), Tehran, Iran.
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Jin P, Wang G, Chen L. Biphasic action potential and chaos in a symmetrical Chua Corsage Memristor-based circuit. CHAOS (WOODBURY, N.Y.) 2023; 33:023120. [PMID: 36859197 DOI: 10.1063/5.0138363] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/11/2022] [Accepted: 01/23/2023] [Indexed: 06/18/2023]
Abstract
Neuromorphic computing provides unique computing and memory capabilities that could break the limitation of conventional von Neumann computing. Toward realizing neuromorphic computing, fabrication and synthetization of hardware elements and circuits to emulate biological neurons are crucial. Despite the striking progress in exploring neuron circuits, the existing circuits can only reproduce monophasic action potentials, and no studies report on circuits that could emulate biphasic action potentials, limiting the development of neuromorphic devices. Here, we present a simple third-order memristive circuit built with a classical symmetrical Chua Corsage Memristor (SCCM) to accurately emulate biological neurons and show that the circuit can reproduce monophasic action potentials, biphasic action potentials, and chaos. Applying the edge of chaos criterion, we calculate that the SCCM and the proposed circuit have the symmetrical edge of chaos domains with respect to the origin, which plays an important role in generating biphasic action potentials. Also, we draw a parameter classification map of the proposed circuit, showing the edge of chaos domain (EOCD), the locally active domain, and the locally passive domain. Near the calculated EOCD, the third-order circuit generates monophasic action potentials, biphasic action potentials, chaos, and ten types of symmetrical bi-directional neuromorphic phenomena by only tuning the input voltage, showing a resemblance to biological neurons. Finally, a physical SCCM circuit and some experimentally measured neuromorphic waveforms are exhibited. The experimental results agree with the numerical simulations, verifying that the proposed circuit is suitable as artificial neurons.
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Affiliation(s)
- Peipei Jin
- Institute of Modern Circuit and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Guangyi Wang
- Institute of Modern Circuit and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
| | - Long Chen
- Institute of Modern Circuit and Intelligent Information, Hangzhou Dianzi University, Hangzhou 310018, China
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Ramasamy M, Kumarasamy S, Srinivasan A, Subburam P, Rajagopal K. Dynamical effects of hypergraph links in a network of fractional-order complex systems. CHAOS (WOODBURY, N.Y.) 2022; 32:123128. [PMID: 36587325 DOI: 10.1063/5.0103241] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/15/2022] [Accepted: 11/14/2022] [Indexed: 06/17/2023]
Abstract
In recent times, the fractional-order dynamical networks have gained lots of interest across various scientific communities because it admits some important properties like infinite memory, genetic characteristics, and more degrees of freedom than an integer-order system. Because of these potential applications, the study of the collective behaviors of fractional-order complex networks has been investigated in the literature. In this work, we investigate the influence of higher-order interactions in fractional-order complex systems. We consider both two-body and three-body diffusive interactions. To elucidate the role of higher-order interaction, we show how the network of oscillators is synchronized for different values of fractional-order. The stability of synchronization is studied with a master stability function analysis. Our results show that higher-order interactions among complex networks help the earlier synchronization of networks with a lesser value of first-order coupling strengths in fractional-order complex simplices. Besides that, the fractional-order also shows a notable impact on synchronization of complex simplices. For the lower value of fractional-order, the systems get synchronized earlier, with lesser coupling strengths in both two-body and three-body interactions. To show the generality in the outcome, two neuron models, namely, Hindmarsh-Rose and Morris-Leccar, and a nonlinear Rössler oscillator are considered for our analysis.
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Affiliation(s)
- Mohanasubha Ramasamy
- Centre for Computational Modeling, Chennai Institute of Technology, Chennai 600069, India
| | - Suresh Kumarasamy
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Ashokkumar Srinivasan
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
| | - Pavithra Subburam
- Department of Biomedical Engineering, Chennai Institute of Technology, Chennai 600069, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, India
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Njitacke Tabekoueng Z, Shankar Muni S, Fonzin Fozin T, Dolvis Leutcho G, Awrejcewicz J. Coexistence of infinitely many patterns and their control in heterogeneous coupled neurons through a multistable memristive synapse. CHAOS (WOODBURY, N.Y.) 2022; 32:053114. [PMID: 35649984 DOI: 10.1063/5.0086182] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/23/2022] [Accepted: 04/18/2022] [Indexed: 06/15/2023]
Abstract
The phenomenon of hidden heterogeneous extreme multistability is rarely reported in coupled neurons. This phenomenon is investigated in this contribution using a model of a 2D FitzHugh-Nagumo neuron coupled with a 3D Hindmarsh-Rose neuron through a multistable memristive synapse. The investigation of the equilibria revealed that the coupled neuron model is equilibrium free and, thus, displays a hidden dynamics. Some traditional nonlinear analysis tools are used to demonstrate that the heterogeneous neuron system is able to exhibit the coexistence of an infinite number of electrical activities involving both periodic and chaotic patterns. Of particular interest, a noninvasive control method is applied to suppress all the periodic coexisting activities, while preserving only the desired chaotic one. Finally, an electronic circuit of the coupled neurons is designed in the PSpice environment and used to further support some results of the theoretical investigations.
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Affiliation(s)
- Zeric Njitacke Tabekoueng
- Department of Electrical and Electronic Engineering, College of Technology (COT), University of Buea, P.O. Box 63, Buea, Cameroon
| | - Sishu Shankar Muni
- School of Fundamental Sciences, Massey University, Palmerston North, Private Bag 4410, New Zealand
| | - Théophile Fonzin Fozin
- Department of Electrical and Electronic Engineering, Faculty of Engineering and Technology (FET), University of Buea, P.O. Box 63, Buea, Cameroon
| | - Gervais Dolvis Leutcho
- Department of Electrical Engineering, École de Technologie Supérieure (ÉTS), Montreal, Quebec H3C1K3, Canada
| | - Jan Awrejcewicz
- Department of Automation, Biomechanics and Mechatronics, Lodz University of Technology, ul. Stefanowskiego 1/15, 90-537 Lodz, Poland
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A New Memristive Neuron Map Model and Its Network’s Dynamics under Electrochemical Coupling. ELECTRONICS 2022. [DOI: 10.3390/electronics11010153] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
A memristor is a vital circuit element that can mimic biological synapses. This paper proposes the memristive version of a recently proposed map neuron model based on the phase space. The dynamic of the memristive map model is investigated by using bifurcation and Lyapunov exponents’ diagrams. The results prove that the memristive map can present different behaviors such as spiking, periodic bursting, and chaotic bursting. Then, a ring network is constructed by hybrid electrical and chemical synapses, and the memristive neuron models are used to describe the nodes. The collective behavior of the network is studied. It is observed that chemical coupling plays a crucial role in synchronization. Different kinds of synchronization, such as imperfect synchronization, complete synchronization, solitary state, two-cluster synchronization, chimera, and nonstationary chimera, are identified by varying the coupling strengths.
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Wang Z, Ramamoorthy R, Xi X, Namazi H. Synchronization of the neurons coupled with sequential developing electrical and chemical synapses. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:1877-1890. [PMID: 35135233 DOI: 10.3934/mbe.2022088] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
There is some evidence representing the sequential formation and elimination of electrical and chemical synapses in particular brain regions. Relying on this feature, this paper presents a purely mathematical modeling study on the synchronization among neurons connected by transient electrical synapses transformed to chemical synapses over time. This deletion and development of synapses are considered consecutive. The results represent that the transient synapses lead to burst synchronization of the neurons while the neurons are resting when both synapses exist constantly. The period of the transitions and also the time of presence of electrical synapses to chemical ones are effective on the synchronization. The larger synchronization error is obtained by increasing the transition period and the time of chemical synapses' existence.
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Affiliation(s)
- Zhen Wang
- Xi'an Key Laboratory of Advanced Photo-electronics Materials and Energy Conversion Device, School of Science, Xijing University, Xi'an 710123, China
- Shaanxi International Joint Research Center for Applied Technology of Controllable Neutron Source School of Science, Xijing University, Xi'an 710123, China
| | - Ramesh Ramamoorthy
- Centre for Artificial Intelligence, Chennai Institute of technology, Chennai, India
| | - Xiaojian Xi
- Xi'an Key Laboratory of Advanced Photo-electronics Materials and Energy Conversion Device, School of Science, Xijing University, Xi'an 710123, China
| | - Hamidreza Namazi
- School of Engineering, Monash University, Selangor, Malaysia
- College of Engineering and Science, Victoria University, Melbourne, Australia
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Zakharova A, Strelkova G, Schöll E, Kurths J. Introduction to focus issue: In memory of Vadim S. Anishchenko: Statistical physics and nonlinear dynamics of complex systems. CHAOS (WOODBURY, N.Y.) 2022; 32:010401. [PMID: 35105142 DOI: 10.1063/5.0082335] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/14/2021] [Accepted: 12/14/2021] [Indexed: 06/14/2023]
Affiliation(s)
- Anna Zakharova
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Galina Strelkova
- Institute of Physics, Saratov State University, 83 Astrakhanskaya Street, Saratov 410012, Russia
| | - Eckehard Schöll
- Institut für Theoretische Physik, Technische Universität Berlin, Hardenbergstr. 36, 10623 Berlin, Germany
| | - Jürgen Kurths
- Potsdam Institute for Climate Impact Research, Telegraphenberg A 31, 14473 Potsdam, Germany
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Mehrabbeik M, Parastesh F, Ramadoss J, Rajagopal K, Namazi H, Jafari S. Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2021; 18:9394-9409. [PMID: 34814351 DOI: 10.3934/mbe.2021462] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Map-based neuronal models have received much attention due to their high speed, efficiency, flexibility, and simplicity. Therefore, they are suitable for investigating different dynamical behaviors in neuronal networks, which is one of the recent hottest topics. Recently, the memristive version of the Rulkov model, known as the m-Rulkov model, has been introduced. This paper investigates the network of the memristive version of the Rulkov neuron map to study the effect of the memristor on collective behaviors. Firstly, two m-Rulkov neuronal models are coupled in different cases, through electrical synapses, chemical synapses, and both electrical and chemical synapses. The results show that two electrically coupled memristive neurons can become synchronous, while the previous studies have shown that two non-memristive Rulkov neurons do not synchronize when they are coupled electrically. In contrast, chemical coupling does not lead to synchronization; instead, two neurons reach the same resting state. However, the presence of both types of couplings results in synchronization. The same investigations are carried out for a network of 100 m-Rulkov models locating in a ring topology. Different firing patterns, such as synchronization, lagged-phase synchronization, amplitude death, non-stationary chimera state, and traveling chimera state, are observed for various electrical and chemical coupling strengths. Furthermore, the synchronization of neurons in the electrical coupling relies on the network's size and disappears with increasing the nodes number.
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Affiliation(s)
- Mahtab Mehrabbeik
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
| | - Fatemeh Parastesh
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
| | - Janarthanan Ramadoss
- Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
| | - Karthikeyan Rajagopal
- Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
| | - Hamidreza Namazi
- School of Engineering, Monash University, Selangor, Malaysia
- College of Engineering and Science, Victoria University, Melbourne, Australia
| | - Sajad Jafari
- Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
- Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
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