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Generalized synchronization of the fractional-order chaos in weighted complex dynamical networks with nonidentical nodes. (English) Zbl 1258.34130

Summary: A fractional-order weighted complex network consists of a number of nodes, which are the fractional-order chaotic systems, and weighted connections between the nodes. In this paper, we investigate generalized chaotic synchronization of the general fractional-order weighted complex dynamical networks with nonidentical nodes. The well-studied integer-order complex networks are the special cases of the fractional-order ones. Based on the stability theory of linear fraction-order systems, the nonlinear controllers are designed to make the fractional-order complex dynamical networks with distinct nodes asymptotically synchronize onto any smooth goal dynamics. Numerical simulations are provided to verify the theoretical results. It is worth noting that the synchronization effect sensitively depends on both the fractional order \(\theta\) and the feedback gain \(k_i\). Moreover, generalized synchronization of the fractional-order weighted networks can still be achieved effectively with the existence of noise perturbation.

MSC:

34D06 Synchronization of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
34A08 Fractional ordinary differential equations
92B20 Neural networks for/in biological studies, artificial life and related topics
34F05 Ordinary differential equations and systems with randomness
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