Abstract
This paper addresses the challenges of achieving polynomial and exponential synchronization in coupled neural networks with proportional delay under Denial of Service (DoS) attacks. We propose a novel control technique, incorporating an event-triggered saturated impulsive control, designed to minimize communication transmission signals. This approach not only effectively mitigates the impact of DoS attacks but also reduces network load while preserving acceptable system performance. Using the matrix measure method and Halanay-type inequalities, we derive sufficient conditions for ensuring polynomial and exponential synchronization in the system. Additionally, numerical simulations are provided to validate the theoretical results in the presence of DoS attacks. For the image encryption algorithm, we utilize a chaotic sequence combined with a scrambling technique based on an enhanced Arnold’s cat map, yielding strong encryption properties that defend against statistical attacks.