Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps

Mahtab Mehrabbeik; Fatemeh Parastesh; Janarthanan Ramadoss; Karthikeyan Rajagopal; Hamidreza Namazi; Sajad Jafari; Mahtab Mehrabbeik; Fatemeh Parastesh; Janarthanan Ramadoss; Karthikeyan Rajagopal; Hamidreza Namazi; Sajad Jafari

doi:10.3934/mbe.2021462

Mathematical Biosciences and Engineering

2021, Volume 18, Issue 6: 9394-9409. doi: 10.3934/mbe.2021462

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Research article Special Issues

Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps

1.
Department of Biomedical Engineering, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran
2.
Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
3.
Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, Tamilnadu-600069, India
4.
School of Engineering, Monash University, Selangor, Malaysia
5.
College of Engineering and Science, Victoria University, Melbourne, Australia
6.
Health Technology Research Institute, Amirkabir University of Technology, No. 350, Hafez Ave, Valiasr Square, Tehran 159163-4311, Iran

Academic Editor: Michele Miglior

Received: 24 September 2021 Accepted: 21 October 2021 Published: 28 October 2021

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.
- synchronization,
- chimera state,
- memristor,
- M-Rulkov map,
- neuronal network
Citation: Mahtab Mehrabbeik, Fatemeh Parastesh, Janarthanan Ramadoss, Karthikeyan Rajagopal, Hamidreza Namazi, Sajad Jafari. Synchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps[J]. Mathematical Biosciences and Engineering, 2021, 18(6): 9394-9409. doi: 10.3934/mbe.2021462

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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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