Spontaneous Activity Induced by Gaussian Noise in the Network-Organized FitzHugh-Nagumo Model.

Qianqian Zheng,Yong Xu,Jianwei Shen,Rubin Wang

doi:10.1155/2020/6651441

Abstract

In this paper, we show some dynamical and biological mechanisms of the short-term memory (the fixed point attractor) through the toggle switch in the FitzHugh-Nagumo model (FN). Firstly, we obtain the bistable conditions, show the effect of Gaussian noise on the toggle switch, and explain the short-term memory's switch mechanism by mean first passage time (MFPT). Then, we obtain a Fokker-Planck equation and illustrate the meaning of the monostable and bistable state in the short-term memory. Furthermore, we study the toggle switch under the interaction of network and noise. Meanwhile, we show that network structure and noise play a vital role in the toggle switch based on network mean first passage time (NMFPT). And we illustrate that the modest clustering coefficient and noise are necessary to maintain memories. Finally, the numerical simulation shows that the analytical results agree with it.

Highlights

Short-term memory is a fundamental cognitive function dependent on persistent activity patterns in populations of neurons, which attributes to a fixed point attractor [1]
To illustrate the dynamical and biological mechanism of the fixed point attractor and neurons in short-term memory, we investigate the FitzHugh-Nagumo model (FN) model’s bistable state with noise and show how the topology structure and noise play a vital role in the switch of a bistable state
Short-term memory attributes to a fixed point attractor, the role of a fixed point attractor was seldom investigated

Summary

Introduction

Short-term memory is a fundamental cognitive function dependent on persistent activity patterns in populations of neurons, which attributes to a fixed point attractor [1]. Some dynamical mechanisms of short-term memory (the fixed point attractor) in neuron activity remain unknown. The toggle switch induced by noise in the network-organized FN model was seldom investigated to explain the dynamical mechanisms of short-term memory (the fixed point attractor). To illustrate the dynamical and biological mechanism of the fixed point attractor and neurons in short-term memory, we investigate the FN model’s bistable state with noise and show how the topology structure and noise play a vital role in the switch of a bistable state. We try to show the effect of Gaussian noise on the toggle switch and try to explain the dynamical mechanism of short-term memory by mean first passage time (MFPT). We try to explain the biological mechanism of short-term memory and dynamical mechanism of neurons through the fixed point attractor

Model Description

Switch Induced by α-Stable Noise

The Network-Organized FN Model with Noise

Conclusion