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Synchronization of delayed complex dynamical networks with impulsive and stochastic effects. (English) Zbl 1223.37115

Authors’ abstract: “In this paper, the globally exponential synchronization of delayed complex dynamical networks with impulsive and stochastic perturbations is studied. The concept named average impulsive interval with elasticity number of impulsive sequence is introduced to get a less conservative synchronization criterion. By comparing with existing results, in which maximum or minimum of impulsive intervals are used to derive the synchronization criterion, the proposed synchronization criterion increases (or decreases) the impulse distances, which leads to the reduction of the control cost (or enhances the robustness of anti-interference) as the most important characteristic of impulsive synchronization techniques. It is discovered in our criterion that the elasticity number has influence on the synchronization of delayed complex dynamical networks but has no influence on that of non-delayed complex dynamical networks. Numerical simulations including a small-world network coupled with delayed Chua’s circuit are given to show the effectiveness and less conservativeness of the theoretical results.”

MSC:

37N35 Dynamical systems in control
34D06 Synchronization of solutions to ordinary differential equations
05C82 Small world graphs, complex networks (graph-theoretic aspects)
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