Lag synchronization of two identical Hindmarsh–Rose neuron systems with mismatched parameters and external disturbance via a single sliding mode controller

This paper presents a systematic design procedure to lag synchronize two identical Hindmarsh–Rose neuron systems based on a sliding mode control. A switching surface only including partial states is adopted to ensure the stability of the error dynamics in the sliding mode. Then an adaptive sliding mode controller is derived to guarantee the occurrence of the sliding motion even when the partial parameters of the drive and response Hindmarsh–Rose neuron systems are unknown. The numerical simulation is presented to verify the effectiveness of the proposed control scheme. It is shown that the proposed adaptive sliding mode control scheme offers several advantages such as the consistent estimation of parameters including large robustness to parameter variations and external disturbances.