Fuzzy-Based Sampled-Data Synchronization of the Hindmarsh–Rose Neuronal Model

This article aims to explore the dynamics involved in the intricate realm of chaotic synchronization in the Hindmarsh–Rose (H–R) neuronal model, which is known for its resemblance to the brain's information-processing components. Distinct from the existing studies related to the H–R neuronal model, this research focuses on addressing nonlinearities of membrane potential through a Takagi–Sugeno (T–S) fuzzy approach. A sampled-data-based controller scheme that can resolve the stabilization issues inherent to the H–R neuronal model is proposed. Compared with many existing control schemes, sampled-data control has several advantages, which include easy digital implementation and robustness against transmission delays. This research utilizes the zero-order holder technique to handle discrete-time control actions in a continuous-time T–S fuzzy model. Furthermore, synchronization analysis pertaining to the T–S fuzzy-based H–R model with user-designed control inputs is conducted to understand and overcome the associated spiking, chaotic, and bursting behaviors. Closed-loop dynamics of the resulting model with and without control input, namely, the error model, are analyzed by employing the Lyapunov stability theory and integral inequalities. Specifically, a suitable Lyapunov Krasovskii functional is formulated and solved using the linear matrix inequalities technique to guarantee the global asymptotically stability of the error model. The developed theoretical framework is validated using numerical simulations, and the corresponding outcomes are graphically illustrated and discussed.