Complete synchronization of coupled Rulkov neuron networks

Sun, Huijing; Cao, Hongjun

doi:10.1007/s11071-016-2654-z

Cited by 28 publications

(8 citation statements)

References 27 publications

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“…In 2016, Sun and Cao [8] reported that the Rulkov neurons cannot reach the synchronous temporal firing pattern when coupled via the electrical synapses/diffusive couplings. Instead, they announced that through the inner linking function f (x, y), coupled Rulkov maps can achieve complete synchrony.…”

Section: Electrochemical Intralayer and Chemical Interlayer Interactionsmentioning

confidence: 99%

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The simplest multilayer network of Rulkov neuron maps: A dynamical analysis under different neuronal interactions

Vivekanandhan¹,

Mirzaei²,

Mehrabbeik³

et al. 2022

EPL

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Dynamical map-based networks have been considered in many scientific fields due to their exciting behaviors while they are of low computational costs and more flexibility. Hence, map-based neuronal networks can be preferable for studying the behavior of brain neurons due to their speed and simplicity. Synchronization, cluster synchronization, and chimera are three essential collective behaviors of neurons that have been noticed in many studies. The simplest multilayer neuronal network, capable of exhibiting synchronization, cluster synchronization, and chimera, is a two-layer network with two neurons in each layer. Considering the dynamics of the Rulkov map as the nodes’ dynamics of the two-layer network, this paper aims to detect the regions of different collective behaviors of the network under different types of intralayer interactions: chemical synapses, electrochemical synapses, electrical synapses, and inner linking functions. In all cases, the interlayer neurons interact through chemical synapses. It is revealed that the considered network can exhibit different neuronal collective behaviors, such as complete synchronization, cluster synchronization, chimera, and asynchronization.

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Section: Electrochemical Intralayer and Chemical Interlayer Interactionsmentioning

confidence: 99%

“…Some additional studies have been done on the Rulkov map. For example, Sun and Cao [8] used the master stability functions to investigate the complete synchronization of electrically coupled Rulkov map neuronal networks. They concluded that complete synchronization could not occur in such (a) E-mail: m.mehrabbeik@gmail.com (corresponding author) networks.…”

mentioning

confidence: 99%

The simplest multilayer network of Rulkov neuron maps: A dynamical analysis under different neuronal interactions

Vivekanandhan¹,

Mirzaei²,

Mehrabbeik³

et al. 2022

EPL

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show abstract

“…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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“…Very few studies in the literature have focused on the synchronization of discrete systems by using MSF. Sun and Cao analyzed the complete synchronization of coupled Rulkov neuron networks with the help of MSF [40]. In [41], the authors have investigated the complete synchronization of a coupled chaotic Aihara neuron network with electrical synapses.…”

Section: Introductionmentioning

confidence: 99%

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

Ramasamy,

Kumarasamy,

Sampathkumar

et al. 2023

Complexity

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In recent times, studies on discrete nonlinear systems received much attention among researchers because of their potential applications in real-world problems. In this study, we conducted an in-depth exploration into the stability of synchronization within discrete nonlinear systems, specifically focusing on the Hindmarsh–Rose map, the Chialvo neuron model, and the Lorenz map. Our methodology revolved around the utilization of the master stability function approach. We systematically examined all conceivable coupling configurations for each model to ascertain the stability of synchronization manifolds. The outcomes underscored that only distinct coupling schemes manifest stable synchronization manifolds, while others do not exhibit this trait. Furthermore, a comprehensive analysis of the master stability function’s behavior was performed across a diverse range of coupling strengths σ and system parameters. These findings greatly enhance our understanding of network dynamics, as discrete-time dynamical systems adeptly replicate the dynamics of continuous-time models, offering significant reductions in computational complexity.

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Complete synchronization of coupled Rulkov neuron networks

Cited by 28 publications

References 27 publications

The simplest multilayer network of Rulkov neuron maps: A dynamical analysis under different neuronal interactions

The simplest multilayer network of Rulkov neuron maps: A dynamical analysis under different neuronal interactions

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

Synchronizability of Discrete Nonlinear Systems: A Master Stability Function Approach

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