Unidirectional synchronization of Morris-Lecar neurons via adaptive H _∞ control

This paper presents an adaptive neural network H_∞ control for unidirectional synchronization of modified Morris-Lecar (ML) neurons in a master-slave configuration. The modified ML neurons exhibit different periods bursting and repetitive spiking in response to electrical stimulation. Based on the Lyapunov stability theory, we derive the update 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 closedloop 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 robustness and effectiveness of the proposed control method.