Synchronization of two identical and non-identical Rulkov models

Sun, Huijing; Cao, Hongjun

doi:10.1016/j.cnsns.2016.04.011

Cited by 15 publications

(3 citation statements)

References 36 publications

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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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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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“…Some others work also involved the computation of the Rulkov's map by improved the model or considering the model in the networks, such as memristive neuron for Rulkov model including magnetic effects [21][22][23]; the synchronization problem of chaotic oscillators [24][25][26][27]; and delayed feedback control of bursting synchronization [28][29][30][31]; phase synchronisation of bursting neurons in small-world networks [32][33][34][35]. Based on the master stability function (MSF) analysis, complete synchronization of two electrical coupled chaotic Rulkov neurons was considered [36]. And by using the knowledge of nonlinear science, some interesting phenomena have been discovered.…”

Section: Introductionmentioning

confidence: 99%

New phenomena in Rulkov map based on Poincaré cross section

Wang,

Zhang,

Liang

2023

Nonlinear Dyn

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Different from analyzing the time-series directly, the Poincaré cross-section method is employed in the dynamical study of the Rulkov mapping model, more importance is that some new phenomena of the model are reported in this paper. First, it is proved that x = −1 is the Poincaré cross-section for all non-converging-to-fixed-point trajectories based on fast-slow dynamics. Then, some new dynamics are presented by means of the Poincaré cross-section method. In detail, a " lightning-shaped" periodic divider of the original model is introduced, which is caused by the different selection of the initial value of slow variable. The Period 3 on the Poincaré cross-section is proposed near the chaos region, which may be not reported in other literatures according to our understanding. In some parameter region, it will cause the pseudo chaos phenomenon, here the trajectories spend a lot time converging to a periodic solution. Besides, in the view of mean-field of action potential, the sensitiveness with small parameter's perturbations is analyzed, which the period changes frequently in the bursts of spikes region, and it has robustness in the normal spikes region.

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“…[44] Thereafter, coherence resonance and stochastic spiking-bursting excitability in the 2D Rulkov model with noise [45,46] and random force were numerically disclosed. [47] Beyond the work of single Rulkov neuron, Rulkov neuron-based networks with electrical and chemical synapse were built, from which the stability and chaos evolution, [48] synchronization of two identical and nonidentical Rulkov models, [49] and rich bursting patterns were numerically investigated. [50,51] All of these literatures were carried out in the numerical survey, but hardware implementation is more important for engineering application.…”

Section: Introductionmentioning

confidence: 99%

Continuous non-autonomous memristive Rulkov model with extreme multistability*

Liu

Feng

et al. 2021

Chinese Phys. B

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Based on the two-dimensional (2D) discrete Rulkov model that is used to describe neuron dynamics, this paper presents a continuous non-autonomous memristive Rulkov model. The effects of electromagnetic induction and external stimulus are simultaneously considered herein. The electromagnetic induction flow is imitated by the generated current from a flux-controlled memristor and the external stimulus is injected using a sinusoidal current. Thus, the presented model possesses a line equilibrium set evolving over the time. The equilibrium set and their stability distributions are numerically simulated and qualitatively analyzed. Afterwards, numerical simulations are executed to explore the dynamical behaviors associated to the electromagnetic induction, external stimulus, and initial conditions. Interestingly, the initial conditions dependent extreme multistability is elaborately disclosed in the continuous non-autonomous memristive Rulkov model. Furthermore, an analog circuit of the proposed model is implemented, upon which the hardware experiment is executed to verify the numerically simulated extreme multistability. The extreme multistability is numerically revealed and experimentally confirmed in this paper, which can widen the future engineering employment of the Rulkov model.

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Synchronization of two identical and non-identical Rulkov models

Cited by 15 publications

References 36 publications

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

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

New phenomena in Rulkov map based on Poincaré cross section

Continuous non-autonomous memristive Rulkov model with extreme multistability*

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