The Application Of Nonlinear System Theory On Chialvo Neuron Model

Nonlinear dynamics,is a subject to study the nonlinear motion law.The main research contents of this thesis include the structural stability,the stability of the trajectory,bifurcation,chaos,and so on.The study of nonlinear dynzamic system not only has significant values in theory,but also has wide application future in scientific research.The nonlinear system involves almost all areas of the natural and social sciences,and its theory and methods have been widely applied in the fields of physics,chemistry,biology,ecology,medical treatment and economics.This thesis mainly considers the application of nonlinear system theory in the nervous system.Based on the Chialvo neuron model,we at first consider the two-dimensional parameter spaces of discrete-time Chialvo neuron model and give the expression of Neimark-Sacker bifurcation curve.For each pair of parameters,the final state of attractor is identified and discussed including periodic,non-finite,quasiperiodic and chaotie.attractors.We display a detail analysis for the bifurcation and dynamic characteristics of periodic attractors embedded in quasi-periodic or chaos.Secondly,the neural network is modeled by connecting Chialvo neurons which are in chaotic spiking state.When lots of irregular individuals are closely linked by linear coupling,dynamic behaviors of the higher dimensional network are described by using qualitative analysis and numerical simulation.It is verified that the neural network can get a stable synchronous fixed point,and the neural network can achieve completely phase synchronization with the changing of coupling strength.Finally,we summarize our work,offering a good foundation for comprehen-sively analyzing the dynamic behaviors of single discrete neuron model and neural network system.