Dynamics Analysis Of Nonlinear Neuron Systems

Neurons are the basic unit of the nervous system, the electrical activity of neurons is the basis ofthe neural electrical activity information system. Neural electrophysiological activity has complexnonlinear dynamics behavior, such as cycle, bifurcation and chaos etc. Neurons in different dischargemodes is an important part of the neuron function for biological activity. Based on the analysis of thecurrent research and summarizes the neuron system, using the theory of fractioal order differentialequations, the stability and bifurcation theory of partial functional differential equations, the stabilityand bifurcation of a class of FHN neuron system are studied. The full text is organized as follows:In the first Chapter of this dissertation, the author elaborates the current status and research thenon-linear neuron system, and expounds the main contents of this paper.The second Chapter analyzes the fractional FHN model with feedback control stability problem,feedback control on the stability of the system are discussed.The third Chapter studies the stability and bifurcation problems of delay FHN systems with andwithout diffusion respectively. In addition, we also study the direction of bifurcation and the existenceand stability of periodic solution.The fourth Chapter summarizes the research work of this dissertation. Furthermore, the futureresearch direction is made.