In this paper, the finite-time stochastic outer synchronization between two different complex dynamical networks with noise perturbation is investigated. By using suitable controllers, sufficient conditions for finite-time stochastic outer synchronization are derived based on the finite-time stability theory of stochastic differential equations. It is noticed that the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. Finally, numerical examples are examined to illustrate the effectiveness of the analytical results. The effect of control parameters on the settling time is also numerically demonstrated.

In this article, we propose a Cucker–Smale‐type self‐propelled particle model with continuous non‐Lipschitz protocol. We show that the flocking can occur in finite time if the communication rate function satisfies a lower bound condition. Both our theoretical and numerical results uncover a power‐law relationship between the convergence time and the number of individuals. Our result implies that the individuals in groups with high density can transit rapidly to ordered collective motion. We also investigate the influence of control parameter on the convergence speed. © 2015 Wiley Periodicals, Inc. Complexity 21: 354–361, 2016

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We study the effect of noise on the outer synchronization between two unidirectionally coupled complex networks and find analytically that outer synchronization could be achieved via white-noise-based coupling. It is also demonstrated that, if two networks have both conventional linear coupling and white-noise-based coupling, the critical deterministic coupling strength between two complex networks for synchronization transition decreases with an increase in the intensity of noise. We provide numerical results to illustrate the feasibility and effectiveness of the theoretical results.