Dynamical Analysis Of The Neuronal Chay Model

Chay model takes the form of three dimensional differential equations group and describes the variation of cell trans-membrane voltage as well as channelized ion current. As Chay model can describes the different patterns of firing of actuarial excitable cell,studying of the Chay model is of great important to understand and predict biological characteristics.The firing action of neuronal have complicated characteristics of dynamical. This thesis based on the Chay model, took parameters Vkand g1, as physical significance.With the aid of algebra criterion of Hopf bifurcation in high dimension equations and the theory of nonlinear dynamics,we did analyses of the bifurcation and investigated the characteristics of model with the variation of parameter.Firstly, by adding current and circle electrical on Chay model, we obtained different firing pattern respond to its parameter though the way of numerical simulation.Then,we added Gaussian white noise on Chay model, got the mechanism of noise on neuronal systems.Finally,we researched the firing of the Chay model under the function of the Gaussian white noise and circle electrical we added.Based on the original research in this thesis, we found the complicated nonlinear dynamic action of neuronal. It showed new light on the biological characteristics in neuronal system.