Control of Hopf Bifurcations in Hodgkin-Huxley Neurons by Automatic Temperature Manipulation

Abstract

The purpose of this research is to revisit the bifurcation control problem in Hodgkin-Huxley neurons. As a difference from the classical membrane potential feedback to manipulate the external current injection, we will actuate the temperature of the neural environment to control the bifurcations. In order to achieve this a linear feedback from the membrane potential is established to generate a time varying temperature profile. The considered bifurcating parameter is the external current injection. Upon finishing the controllers, the bifurcation analysis against the changes in external current injection is repeated in order to see the possibility of relapse of any bifurcation phenomena at nearby points. In addition to that, simulations are also provided to show the performances of the controllers.