Open AccessSynchronization and chimera states in the network of electrochemically coupled memristive Rulkov neuron maps
Author(s) -
Mahtab Mehrabbeik,
Fatemeh Parastesh,
Janarthanan Ramadoss,
Karthikeyan Rajagopal,
Hamidreza Namazi,
Sajad Jafari
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021462
Subject(s) - memristor , electrical synapses , synchronization (alternating current) , topology (electrical circuits) , chimera (genetics) , coupling (piping) , synchronization networks , computer science , neuron , biological neuron model , biological neural network , biological system , network model , physics , neuroscience , artificial neural network , artificial intelligence , materials science , chemistry , engineering , biology , electrical engineering , intracellular , biochemistry , quantum mechanics , metallurgy , gap junction , gene , machine learning
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.