Stabilizing control of Hopf bifurcation in the Hodgkin–Huxley model via washout filter with linear control term

Abstract

It is a significant issue to control bifurcation because many neuronal diseases have close relevance to bifurcation of neuron system. Some studies have been done on bifurcation control in the Hodgkin–Huxley (HH) model, but there is no clear mathematical criterion for bifurcation stabilization. In this paper, according to Routh–Hurwitz stability criterion, we employ linear control term of washout filter-aided dynamic feedback controller to stabilize bifurcation of the HH model. As a result, we can deduce linear control gain based on the criterion, and simulation shows the method is effective for making the HH model stable. The controller designs described here are achieved by electrical stimulus, so it may have potential applications in the diagnosis and therapy of dynamical diseases.