Unidirectional synchronization of Hodgkin-Huxley neurons exposed to ELF electric field

In this paper, a hybrid control strategy, H∞ variable universe adaptive fuzzy control, is derived and applied to synchronize two Hodgkin-Huxley (HH) neurons exposed to external electric field. Firstly, the modified model of HH neuron exposed to extremely low frequency (ELF) external electric field is established and its periodic and chaotic dynamics in response to sinusoidal electric field stimulation are described. And then the statement of the problem for unidirectional synchronization of two HH neurons is given. Finally H∞ variable universe adaptive fuzzy control is designed to synchronize the HH systems and the simulation results demonstrate the effectiveness of the proposed control method.