Bifurcation control of a fractional order Hindmarsh-Rose neuronal model

Abstract

This paper proposes to use a state feedback method to control the Hopf bifurcation for a fractional order Hindmarsh-Rose neuronal model. The order of the fractional order Hindmarsh-Rose neuronal model is chosen as the bifurcation parameter. The analysis shows that in the absences of the state feedback controller, the fractional order model loses stability via the Hopf bifurcation early, and can maintain the stability only in a certain domain of the gain parameter. When applying the state feedback controller to the model, the onset of the undesirable Hopf bifurcation is postponed. Thus, the stability domain is extended, and the model possesses the stability in a larger parameter range. Numerical simulations are given to justify the validity of the state feedback controller in bifurcation control. © 2013 Springer-Verlag Berlin Heidelberg.