Analysis and control of the bifurcation in a Morris-Lecar neuron via a washout filter-aided dynamic control law

The bifurcation phenomena in the neuronal system are known as to cause many neuronal diseases such as epilepsy, Alzheimer's disease, Parkinson's disease, or schizophrenia, etc. Therefore, understanding the dynamics and manipulation of bifurcation characteristics of the neuronal system are promising to provide diagnostic and therapy trajectories for these diseases. In this paper, we address the problem of bifurcation control of a Morris-Lecar (ML) neuron model. First, we analysis the dynamic behavior of a ML model, the stability of equilibrium points and the occurrence of Hopf bifurcations in the ML model are investigated. Second, we employ a washout filter-aided dynamic control law to achieve two bifurcation control objectives: stabilize the original Hopf bifurcation point and advance the Hopf bifurcation point toward a desired point. Finally, in order to verify the effectiveness of the proposed methods, numerical simulations are performed, the results of which are provided herein.