Stability and synchronization of coupled Rulkov map-based neurons with chemical synapses

A theoretical model of a network of neuron-like elements was constructed. The network included several subnetworks. The first subnetwork was used to translate a constant-amplitude signal into a spike sequence (conversion of amplitude to frequency). A similar process occurs in the brain when perceiving visual information. With an increase in the flow of information, the generation frequency of the neural ensemble participating in the processing increases. Further, the first subnetwork transmitted excitation to two large interconnected subnetworks. These subnetworks simulated the dynamics of the cortical neuronal populations. It was shown that in the presence of inhibitory coupling, the neuronal ensembles demonstrate antiphase dynamics. Various connectivity topologies and various types of neuron-like oscillators were investigated. We compare the results obtained in a discrete neuron model (Rulkov model) and a continuous-time model (Hodgkin-Huxley). It is shown that in the case of a discrete neuron model, the periodic dynamics is manifested in the alternate excitation of various neural ensembles. In the case of the continuous-time model, periodic modulation of the synchronization index of neural ensembles is observed.

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“…β syn and σ syn are coefficients of chemical synaptic coupling [Hu and Cao, 2016], and I syn n is a synaptic current (1)…”

Section: Mathematical Modelmentioning

confidence: 99%

Synchronization in coupled neural network with inhibitory coupling

Андреев

Maksimenko

2019

CAP

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“…Extensive studies [13][14][15][16][17][18] proved that discrete neuron models, especially the Rulkov neuron, could more effectively mimic the real behaviors of biological neurons. On this foundation, Cao et al [19][20][21][22][23] disclosed two identical Rulkov neurons coupled with chemical and electrical synapses, respectively, and reported the influence of the coupling strength on synchronization in detail. By constructing a small-world network made up of Rulkov neurons, Ferrari et al [24] proposed the idea of using delayed feedback to suppress synchronization.…”

Section: Introductionmentioning

confidence: 99%

Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor

et al. 2023

Fractal Fract

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In order to enrich the dynamic behaviors of discrete neuron models and more effectively mimic biological neural networks, this paper proposes a bistable locally active discrete memristor (LADM) model to mimic synapses. We explored the dynamic behaviors of neural networks by introducing the LADM into two identical Rulkov neurons. Based on numerical simulation, the neural network manifested multistability and new firing behaviors under different system parameters and initial values. In addition, the phase synchronization between the neurons was explored. Additionally, it is worth mentioning that the Rulkov neurons showed synchronization transition behavior; that is, anti-phase synchronization changed to in-phase synchronization with the change in the coupling strength. In particular, the anti-phase synchronization of different firing patterns in the neural network was investigated. This can characterize the different firing behaviors of coupled homogeneous neurons in the different functional areas of the brain, which is helpful to understand the formation of functional areas. This paper has a potential research value and lays the foundation for biological neuron experiments and neuron-based engineering applications.

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“…Many applications of single-neuron models already exist, but it seems that a systematic study of their response as a function of the control parameters lack. Map-based models are easier to treat and analyze and have been used to describe specific situations, especially when considering coupled elements characterized by chemical [28,29], electrical [30,31] or both aspects [32][33][34][35]. The topology of neural networks is also an essential player in their dynamical behavior, as reported for, e.g., scalefree [32], global [36], mean-field [37], small world [38], and Apollonian [39,40] networks.…”

Section: Introductionmentioning

confidence: 99%

Distribution of spiking and bursting in Rulkov’s neuron model

Ramírez-Ávila

Depickère

Jánosi

et al. 2022

Eur. Phys. J. Spec. Top.

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Large-scale brain simulations require the investigation of large networks of realistic neuron models, usually represented by sets of differential equations. Here we report a detailed fine-scale study of the dynamical response over extended parameter ranges of a computationally inexpensive model, the two-dimensional Rulkov map, which reproduces well the spiking and spiking-bursting activity of real biological neurons. In addition, we provide evidence of the existence of nested arithmetic progressions among periodic pulsing and bursting phases of Rulkov’s neuron. We find that specific remarkably complex nested sequences of periodic neural oscillations can be expressed as simple linear combinations of pairs of certain basal periodicities. Moreover, such nested progressions are robust and can be observed abundantly in diverse control parameter planes which are described in detail. We believe such findings to add significantly to the knowledge of Rulkov neuron dynamics and to be potentially helpful in large-scale simulations of the brain and other complex neuron networks.

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Stability and synchronization of coupled Rulkov map-based neurons with chemical synapses

Cited by 36 publications

References 35 publications

Synchronization in coupled neural network with inhibitory coupling

Synchronization in coupled neural network with inhibitory coupling

Multistability and Phase Synchronization of Rulkov Neurons Coupled with a Locally Active Discrete Memristor

Distribution of spiking and bursting in Rulkov’s neuron model

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