Stability and Bifurcation of a Neuron Model with Delay-Dependent Parameters

摘要

An analytical method is proposed to study the dynamics of a neuron model with delay-dependent parameters. Stability and bifurcation of this model are analyzed using stability switches and Hopf bifurcation proposition. A series of critical time delay are determined and a simple stable criterion is given according to the range of parameters. Through the analysis for the bifurcation, it is shown that a very large delay could also stabilize the system. This conclusion is quite different from that of the system with only delay-independent parameters.