Bifurcation Control of Hodgkin-Huxley model of nerve system

Abstract

Bifurcation control has attracted increasing attention in recent years. It deals with the modification of the bifurcation characteristics of a parameterized nonlinear system by a judiciously designed control input. In this paper, we consider the problem of dynamic feedback control of bifurcations. The object we study is the Hodgkin-Huxley (HH) equations. Here we analyse two kinds of bifurcation in HH equations and use two different control methods to eliminate bifurcations. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.