Stochastic multi-resonance induced by partial time delay in a Watts-Strogatz small-world neuronal network

Sun Xiao-Juan;  Li Guo-Fang

doi:10.7498/aps.65.120502

How electromagnetic induction and coupled delay affect stochastic resonance in a modified neuronal network subject to phase noise

International Journal of Modern Physics B ◽

10.1142/s0217979219503028 ◽

2019 ◽

Vol 33 (26) ◽

pp. 1950302

Author(s):

Xiao Li Yang ◽

Xiao Qiang Liu

Keyword(s):

Time Delay ◽

Phase Noise ◽

Stochastic Resonance ◽

Neuronal Network ◽

Electromagnetic Induction ◽

Small World ◽

Feedback Gain ◽

Small World Network ◽

Induced Current ◽

Resonance Response

Through introducing the ingredients of electromagnetic induction and coupled time delay into the original Fitzhugh–Nagumo (FHN) neuronal network, the dynamics of stochastic resonance in a model of modified FHN neuronal network in the environment of phase noise is explored by numerical simulations in this study. On one hand, we demonstrate that the phenomenon of stochastic resonance can appear when the intensity of phase noise is appropriately adjusted, which is further verified to be robust to the edge-added probability of small-world network. Moreover, under the influence of electromagnetic induction, the phase noise-induced resonance response is suppressed, meanwhile, a large noise intensity is required to induce stochastic resonance as the feedback gain of induced current increases. On the other hand, when the coupled time delay is incorporated into this model, the results indicate that the properly tuned time delay can induce multiple stochastic resonances in this neuronal network. However, the phenomenon of multiple stochastic resonances is found to be restrained upon increasing feedback gain of induced current. Surprisingly, by changing the period of phase noise, multiple stochastic resonances can still emerge when the coupled time delay is appropriately tuned to be integer multiples of the period of phase noise.

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Effects of hybrid synapses and partial time delay on stochastic resonance in a small-world neuronal network

Acta Physica Sinica ◽

10.7498/aps.66.240501 ◽

2017 ◽

Vol 66 (24) ◽

pp. 240501

Author(s):

Li Guo-Fang ◽

Sun Xiao-Juan

Keyword(s):

Time Delay ◽

Stochastic Resonance ◽

Neuronal Network ◽

Small World

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Effects of Time Delay on Burst Synchronization Transition of Neuronal Networks

International Journal of Bifurcation and Chaos ◽

10.1142/s0218127418501432 ◽

2018 ◽

Vol 28 (12) ◽

pp. 1850143 ◽

Cited By ~ 2

Author(s):

Xiaojuan Sun ◽

Tianshu Xue

Keyword(s):

Time Delay ◽

Neuronal Network ◽

Coupling Strength ◽

Neuronal Networks ◽

The Other ◽

Electrical Synapses ◽

Synchronization Transition ◽

Burst Synchronization ◽

Chemical Synapses ◽

Bursting Activity

In this paper, we focus on investigating the effects of time delay on burst synchronization transitions of a neuronal network which is locally modeled by Hindmarsh–Rose neurons. Here, neurons inside the neuronal network are connected through electrical synapses or chemical synapses. With the numerical results, it is revealed that burst synchronization transitions of both electrically and chemically coupled neuronal networks could be induced by time delay just when the coupling strength is large enough. Meanwhile, it is found that, in electrically and excitatory chemically coupled neuronal networks, burst synchronization transitions are observed through change of spiking number per burst when coupling strength is large enough; while in inhibitory chemically coupled neuronal network, burst synchronization transitions are observed for large enough coupling strength through changing fold-Hopf bursting activity to fold-homoclinic bursting activity and vice versa. Namely, two types of burst synchronization transitions are observed. One type of burst synchronization transitions occurs through change of spiking numbers per burst and the other type of burst synchronization transition occurs through change of bursting types.

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