Hopf bifurcation of the fractional-order Hindmarsh–Rose neuron model with time-delay

Abstract

The Hopf bifurcation problem of the fractional-order Hindmarsh–Rose neuron model with time-delay is investigated. The effects of time-delay to the bifurcation behavior of system is considered by linearizing the system at the equilibria method. With the bifurcation theory, the condition for the existence of Hopf bifurcation is obtained when considering time-delay $\tau$ as variable parameter. As illustrated by the numerical example, the proposed theoretical results work effectively and accurately.