Asynchronous intermittent control strategy for stability of stochastic delayed complex networks with deception attacks based on Dupire’s functional Itô formula

This paper investigates the mean-square exponential stability of stochastic delayed complex networks under asynchronous intermittent control with deception attacks (AICDA). Because different nodes have different dynamics, each node requires its own independent intermittent control. Meanwhile, sensor–controller and controller–actuator channels may suffer from deception attacks. The asynchrony makes traditional Halanay inequality methods inapplicable. To overcome this difficulty, we introduce an auxiliary timer for each node, which increases during working intervals and decreases during resting intervals-opposite to the system’s energy trend. By incorporating this timer into a Lyapunov functional and applying Dupire’s functional Itô formula together with graph theory, we unify the negative definiteness of the operator across all intervals, ensuring network stability. The theoretical results are applied to a class of Cohen–Grossberg neural networks, and numerical simulations verify the effectiveness.