P-Bifurcation of Stochastic van der Pol Model as a Dynamical System in Neuroscience  

作　　者：F.S.Mousavinejad M.FatehiNia A.Ebrahimi 

机构地区：[1]Faculty of Mathematical Sciences,Yazd University,Yazd,Iran

出　　处：《Communications on Applied Mathematics and Computation》2022年第4期1293-1312,共20页应用数学与计算数学学报（英文）

摘　　要：This study aims to determine the phenomenological bifurcation(P-bifurcation)occur-ring in the van der Pol(VDP)neuronal model of burst neurons with a random signal.We observe the P-bifurcation under an intense noise stimulus which would become chaotic transitions.Bursting and spiking simulations are used to describe the causes of chaotic transitions between two periodic phases that are the reason for the neuronal activities.Ran-domness plays a crucial role in detecting the P-bifurcation.To determine the equilibrium points,stability or instability of the stochastic VDP equation,and bifurcation,we use the stochastic averaging method and some related theorems.Apart from theoretical methods,we also examine numerical simulations in the particular case of that stochastic equation that illustrates the outcome of theorems for various noise types.The most striking part of our theoretical findings is that these results are also valid for the Izhikevich-FitzHugh model,Bonhoeffer-van der Pol oscillator in dynamical systems of neuroscience.Finally,we will discuss some applications of the VDP equation in neuronal activity.

关 键 词：Averaging diffusion system P-bifurcation Stability NEUROSCIENCE VDP stochastic equation 

分 类 号：O17[理学—数学]