SYNCHRONIZATION ANALYSIS OF DRIVE-RESPONSE MULTI-LAYER DYNAMICAL NETWORKS WITH ADDITIVE COUPLINGS AND STOCHASTIC PERTURBATIONS

摘要

This paper concerns the synchronization of a kind of drive-responsemulti-layer dynamical networks with additive couplings and stochastic perturbations.Multi-layer networks are a kind of complex networks with differentlayers, which consist of different kinds of interactions or multiple subnetworks.Additive couplings are designed to capture the different layered connections. Inthis paper, two pinning controllers are designed to guarantee the synchronizationof the stochastic multi-layer network. One is the state-feedback pinningcontroller with constant control gains. The other one is the adaptive pinningcontroller with adaptive control gains. It is worthwhile to mention that ourassumptions on the activation functions satisfy a generalized Lipschitzian conditionwhich are weaker than those in the previous works. Moreover, as weprove, only selected part of the nodes to be controlled are enough to guaranteethat the drive system and response network can be stochastically synchronized.Finally, an example and its simulations are presented to show the feasibilityeectiveness of our control schemes.