Variable-level pinning impulsive strategy for intra-layer quasi-synchronization of heterogeneous multiplex networks under DoS attacks
摘要
This paper investigates the intra-layer quasi-synchronization (ILQS) of heterogeneous multiplex networks (HMNs) subject to denial-of-service (DoS) attacks, where node dynamics within the same layer are nonidentical. For the first time, a novel variable-level pinning impulsive control (VPIC) scheme is proposed, which applies control only to a subset of state variables with the largest absolute errors at each impulsive instant rather than controlling all variables of the selected nodes, thereby improving upon existing results. A new impulsive differential inequality approach is introduced to derive sufficient conditions for achieving ILQS, and the effects of inter-layer coupling strength, the proportion of controlled variables, and DoS attack parameters on synchronization are further analyzed. Moreover, an upper bound on the synchronization error is given, and the exponential convergence rate is estimated. Numerical simulations are provided, along with a comparison with traditional pinning impulsive control, to illustrate the effectiveness and superiority of the proposed VPIC.