Generalized Synchronization of Complex Neuron Networks in Driver‐Response Configuration for Chaotic Processes

This paper presents the generalized synchronization of neuronal networks in a unidirectionally coupled drive‐response system with interconnected nodes exhibiting chaotic behavior. The study focuses on the synchronization of the Hindmarsh–Rose (HR) neuronal mathematical model through connections among the output, input, and hidden layers. Based on the classical Lyapunov method, sufficient conditions are proposed to synchronize HR neuronal networks using appropriate coupling parameters. The results are derived from classical Lyapunov theory, which employs a continuous time chaotic response system to monitor synchronized dynamics. It is shown that the proposed approach is capable of establishing a response network that achieves generalized synchronization with the drive system via controller design, without relying on dynamic cancelation or feedback. Finally, several simulation examples are presented to demonstrate the feasibility of generalized synchronization in HR neuronal networks.