Reducing And Bifurcation Analyse Of The Neuron Model

Under the external suimulation, neural system, which has complex dynamical character, produces various types of action potential. Neural system is a network which composed by lot of neurons. It can transmit and deal with the neural information. The research of neuron and nerual network is heplful for us to comprehend the function of cerebra and the conduction and effect of acupuncture electrical signal.This paper mainly discusses the reducing of single neuron model, and then analyzes the stability of fixed points and the bifurcation phenomenon of the reduced model. Neuron is a complicated nonlinear dynamical system.The dynamical character can be described to dozens of dimensions. In this paper, we use the nonlinear dynamical method, implement the reducing of nerual model, and then research the dynamical character of the reduced model.The dynamical character of the reduced model is similar with the original model, but it can make the neural network ,which composed by the nerual cells , become very simple. So we can analyze the model well. Using the fact that the evolvement velocity of the variable in the model is diffenrnt, this paper firstly reduces the model from four dimensions to two dimensions. Then, according the classify method of neuron models which introduced by Izhikevich, we classify the reduced model to one of the six minimal models.On the base of the reduced model, this paper analyse the nonliner dynamical character of the model.According to analysis, High-Threshold model has three fixed points in the whole phase space, but it can not occour hopf bifurcation. The Low-Threshold model only has one fixed point in the phase space, and it can occour hopf bifurcation with the change of external current, the lake conductance and the natrium ion reverse potential.The research of this paper can provide some idea for the research of nerual information trainmit and nerual system.