Unidirectional synchronization for Hodgkin-Huxley neurons and parameters identification with adaptive control algorithm

This paper presents an adaptive control algorithm for unidirectional synchronization of two Hodgkin-Huxley (H-H) neurons. The H-H neuron exhibits different periods bursting in response to electrical stimulation. Based on the Lyapunov stability theory, we derive the error estimation and adaptive control method. With the help of the adaptive method mentioned in this article, we can adjust the abnormal H-H neuron to normal state. Besides, by adjusting the adaptive laws, we solve the overshoot problem during the process of parameter identification and successfully identify the error between the abnormal parameters in the abnormal neuron and the normal ones in the reference neuron. Under the effect of adaptive controller, the two neurons can achieve synchronization and the abnormal parameters of unknown neuron are accurately adjusted to normal state. This can be used to cure some diseases caused by abnormal neuron with abnormal parameters. The simulation results demonstrate the correctness and effectiveness of the proposed method.