Abstract
In this paper, the mean-square asymptotical heterogeneous synchronization of interdependent networks with stochastic disturbances, which is a zero-mean real Wiener process, is investigated. The network discussed consists of two sub-networks, which are one-by-one inter-coupled. The unknown but bounded nonlinear coupling functions not only exist in the intra-coupling but also in the inter-coupling between two sub-networks. Based on the stochastic Lyapunov stability theory, adaptive control, Itô formula and the linear matrix inequality, several sufficient conditions are proposed to guarantee adaptive mean-square heterogeneous asymptotical synchronization of the interdependent networks. In order to better illustrate the feasibility and effectiveness of the synchronization conditions derived in this brief, numerical simulations are provided finally.
Highlights
1 Introduction Interdependent networks are a special form of complex networks which are coupled by two or more sub-networks
In Ref. [9], the authors explored the local adaptive heterogeneous synchronization for interdependent networks with delayed coupling consisting of two sub-networks
In which L0, L1, L2 and L3 are constant matrices with suitable dimensions, λ1 and λ2 are the maximum eigenvalues of the matrix P and Q, respectively, the interdependent networks (1) can obtain adaptive mean-square heterogeneous asymptotical synchronization under the control law
Summary
Interdependent networks are a special form of complex networks which are coupled by two or more sub-networks. [9], the authors explored the local adaptive heterogeneous synchronization for interdependent networks with delayed coupling consisting of two sub-networks. Motivated by the above-mentioned issues, in this paper, we discuss the synchronization of interdependent networks with stochastic disturbances.
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