Pinning impulsive control for quasi-projective synchronization of stochastic multi-layer networks

Abstract

This article explores the quasi-projective synchronization of multi-layer coupled neural networks employing pinning impulsive control. First, the network model incorporates intra- and inter-layer couplings while accounting for practical factors such as stochastic disturbances, leakage delay, and heterogeneous nodes. Second, to reduce control costs, we propose a pinning impulsive control strategy that applies impulses to key nodes. Moreover, a delayed pinning impulsive strategy is developed to address the potential delay in the controller's response. Then, utilizing stochastic differential equations and the comparison principle, quasi-projective synchronization conditions are gained and error bounds are accurately computed. Finally, numerical examples involving three-layer networks, along with comparative experiments, are provided to validate the theoretical findings.