Research for Hopf bifurcation of an inertial two-neuron system with time delay

Abstract

The inertia can be considered a useful tool that is added to help in the generation of chaos in neural systems. So it can be added to the standard Hopfield equation. This paper is concerned with a study of the influence of a time delay occurring in a two-inertial neuron system .It is found that as the time delay increases beyond a critical value, the equilibrium position of the inertial two-neuron system becomes unstable and may have Hopf bifurcation. Using the time delay as a bifurcation parameter, Hopf bifurcation is studied by using theory of retarded functional differential equations, then necessary and sufficient conditions for Hopf bifurcation to occur are derived.