Synchronization of nonlinear neural networks with hybrid couplings and uncertain time-varying perturbations: A novel distributed-delay impulsive comparison principle

This paper investigates the synchronization of nonlinear drive-response neural networks subject to uncertain time-varying perturbations, non-delayed coupling, and distributed delay coupling. To address the influence of distributed and discrete delays on the system, we establish a novel impulsive comparison principle, extending the Halanay inequality. By leveraging Lyapunov stability theory, we derive sufficient conditions for the exponential synchronization of the neural networks using a delayed impulsive controller with historical status information. This approach relaxes the conventional constraint that impulsive delays must be smaller than impulsive intervals, thereby generalizing existing synchronization results for distributed delay networks. Numerical simulations for chaotic neural networks validate the theoretical results and demonstrate the sensitivity of the control gain matrix.