Stability analysis and Hopf-type bifurcation of a fractional order Hindmarsh-Rose neuronal model

Abstract

In this paper, the dynamical behaviors of a fractional order Hindmarsh-Rose neuronal model are studied. First, based on the stability theory of fractional order systems, some sufficient conditions for the stability and Hpof-type bifurcation are given for such fractional order system. Then, the frequency and amplitude of periodic oscillations are determined by numerical simulations. It is shown that the frequency of oscillations incurs a small variation with respect to different values of the order, while the amplitude of oscillations gets larger as the order is increased. Numerical simulations are performed to verified the theoretical results. © 2012 Springer-Verlag.