Hopf bifurcation of the fractional-order Hindmarsh-Rose neuron model with time-delay (Q2219131)

In this paper, the authors replace the regular derives in the three-dimensional Hindmarsh-Rose ODE neuron model to fractional derivatives of order and also incorporate a discrete time delay, leading in a so-called fractional-order Hindmarsh-Rose neuron model with time-delay. They then perform a standard Hopf bifurcation analysis for fractional DEs on the resulted model system, using the time delay as the bifurcation parameter. The analysis allows them to obtain some conditions for the existence of Hopf bifurcation. They also provide some numerical example to support their analytic results.