Bifurcation control of the Hodgkin–Huxley equations

The Hodgkin–Huxley equations (HH) are parameterized by a number of parameters and show a variety of qualitatively different behaviors. This paper finds that when the externally applied current Iext varies the bifurcation would occur in the HH equations. The HH model’s Hopf bifurcation is controlled by permanent or interval Washout filters (WF), which can transform the subcritical bifurcations into supercritical bifurcations, and can make the HH equations stable directly. Simulation results show the validity of those controllers. We choose the membrane voltage V as an input to the washout filter because V can be readily measured, and the controller can be realized easily. The controller designs described here may boost the development of electrical stimulation systems for patients suffering from different neuron-system dysfunctions.