Double-integral noise-tolerant gradient neural dynamics: Robust synchronization of Chua’s circuits and video encryption

As secure communication applications grow, chaotic system synchronization has become a fundamental challenge. Environmental noise significantly degrades synchronization accuracy. Meanwhile, mainstream controllers address these perturbations using excessively large control inputs, severely limiting their reliability. To address these challenges, the Chua’s circuit system (CCS) is investigated as a representative model. For its robust synchronization, we propose a double-integral noise-tolerant gradient neural dynamics (DINTGND) model. By incorporating a double-integral error feedback mechanism into the GND framework, the proposed model effectively suppresses quadratic polynomial noise while maintaining low control effort. Rigorous theoretical analysis establishes the DINTGND model’s zero-error convergence under constant and linear noises, and its bounded steady-state error under quadratic noise. Extensive comparisons under quadratic polynomial noise conditions further validate its superior synchronization accuracy and robustness over existing baselines. Furthermore, a novel frame-by-frame video encryption simulation platform (DINTGND-VES) is developed to evaluate the synchronized CCS in noisy scenarios. Finally, these simulations validate that the DINTGND model facilitates robust and high-fidelity video decryption, demonstrating its substantial potential for reliable secure communications.