Synchronization of Uncertain Delayed Complex Dynamical Networks Under Random Impulsive Control and Its Application to Secure Image Communication

ABSTRACT This work examines the synchronization requirements for uncertain delayed complex dynamical networks (UDCDNs) under random impulsive control (RIC), such as moment robust exponential synchronization (RES) and moment exponential synchronization (ES). It proves a new lemma based on random impulsive scalar delay differential inequality by means of sample path approach. Utilizing this inequality, certain unique synchronization requirements for the suggested UDCDNs with the effective control benefits in terms of linear matrix inequalities (LMI) via the Lyapunov function are derived. Chua's N‐node circuit is checked for synchronization using the suggested RIC. Validation is achieved by the use of numerical examples and graphical simulations. Moreover, the chaotic behaviour of error networks in dynamical systems has been employed in secure image communication using encryption. The applications across all cases have been demonstrated and validated, confirming that the models are well‐suited for secure image communication.