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, It? 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.
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