Washout filter based control for the Hodgkin-Huxley nerve cell dynamics

In this work we present a washout filler based control approach for stabilizing the oscillations in Hodgkin-Huxley type neurons. The oscillations occur due to the bifurcations that arise from the potassium and sodium channel conductance deviations. The MATCONT toolbox software environment was used for analysis of the bifurcation points in conjunction with MATLAB. The simulations of the Hodgkin-Huxley (HH) model at those points are provided to validate the results obtained from, the MATCONT software. Then a washout filter is proposed to stabilize the oscillations occur at the Hopf bifurcation points where the external current injection is used to provide the control actuation. A second simulation set is provided to demonstrate the action of the washout filter.