Dynamics Of The Chaotic Rulkov Neuron With Periodic Disturbance

Neuron,which is the basic element of nervous system,is a highly structured cell.One of the famous neuron models is the chaotic Rulkov discrete-time model which can describe many behaviors of the real biological neuron.This map has been widely applied to different fields especially in the computational neuroscience.In recent years,many efforts have been devoted to the control by adding periodic disturbance in nonlinear dynamical systems.In this thesis,we mainly investigate the effect of an external periodic disturbance on a discrete-time Rulkov model.By changing the angular frequency of the external periodic disturbance,the parameter plane is numerically computed in order to examine the order-chaos transition,which is observed by the windows of periodicity embedded in a chaotic region.The numerical simulations exhibit the very rich dynamical behaviors of the forced system when the angular frequency is increased.This thesis is divided to four chapters.The first chapter introduces the background literature related to this paper.The second chapter discusses the influence of periodic disturbance based on Rulkov map model.By changing the external periodic perturbation frequencies,the parameter plane is discussed in detail.In the two-dimensional parameter plane,we found a shrimp type periodic region embedded in a chaotic region,in which the parameter plane can be observed in the period-doubling bifurcation structure from periodic region to periodic regional organizations to separate the shrimp region in each period.Chaos can be seen as a result of suppressing periodic windows embedded in the chaotic region.The third chapter analyses the data by checking whether the results in the second chapter are correct.The final chapter gives a summary of the research.