No-chattering sliding mode control chaos in Hindmarsh–Rose neurons with uncertain parameters

A Hindmarsh–Rose (HR) model was constructed from voltage clamp data to provide a simple description of the patterned activity seen in molluscan neurons. Its complex dynamics characters are presented, including the phase trajectory, the Lyapunov exponents and the Poincaré map. Furthermore, a no-chattering sliding mode control method for the Hindmarsh–Rose (HR) model with uncertain parameters and bounded external disturbances is proposed, and it can control the system to any point and any periodic orbit. Both the theoretical analysis and the simulation results are presented to confirm the validity of the control method.