Synchronization control of Hodgkin-Huxley neurons exposed to ELF electric field

This paper presents an adaptive neural network H_∞ control for unidirectional synchronization of modified Hodgkin-Huxley (HH) neurons exposed to extremely low frequency (ELF) electric field. The proposed modified HH neurons exhibit periodic and chaotic dynamics in response to sinusoidal electric field stimulation. Based on the Lyapunov stability theory, we derive the updated laws of neural network for approximating the nonlinear uncertain functions of the error dynamical system. The H_∞ design technique makes the controller robust to unmodeled dynamics, disturbances and approximate errors. The proposed controller not only ensures closed-loop stability, but also guarantees an H_∞ performance for the synchronization error system. The states of the controlled slave system exponentially synchronize with that of the master one after control. The simulation results demonstrate the validity of the proposed method.