An Efficient Method for Hopf Bifurcation Control in Fractional-Order Neuron Model

Abstract

The nervous system contains a neural network that regulates and coordinates all physiological processes in our body, and as we all know, the damages within the system would lead to many neurological diseases, such as epilepsy, Alzheimer's disease, and Parkinson's disease or schizophrenia. The bifurcation phenomenon in the neuronal system is believed to be the cause, and thus, it is important to understand the mechanism and find effective methods to resist. Several control methods have been proved useful in the integer-order neuronal model. In this paper, we presented a novel control method based on a fractional-order washout filter with time delay for Hopf bifurcation control in a fractional-order neuron model, demonstrating and testing by a fractional-order Hodgkin-Huxley neuron model. The computer simulation shows the effectiveness of the proposed method. Furthermore, we presented the bifurcation phenomenon of fractional-order Hodgkin-Huxley neuron model with the decrease of the order and analyzed the influence of the fractional-order washout filter gain on the Hopf bifurcation of the different order Hodgkin-Huxley neuron model.