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He, Guangming; Yang, Jingyu

Adaptive synchronization in nonlinearly coupled dynamical networks. (English) Zbl 1154.93424

Chaos Solitons Fractals 38, No. 5, 1254-1259 (2008).
Summary: Recently, it has been demonstrated that many large-scale complex dynamical networks display a collective synchronization motion. In this paper, synchronization in nonlinearly coupled dynamical networks is studied. By using the invariance principle of differential equations, some simple linear feedback controllers with dynamical updated strengths are constructed to make the dynamical network synchronize with an isolate node. The feedback strength can be automatically enhanced to make the dynamical network collectively synchronized. The structure of the network can be random, regular, small-world, or scale-free. A numerical example is given to demonstrate the validity of the proposed method, in which the famous Lorenz system is chosen as the node of the network.

Cited in 18 Documents

MSC:

93D21 Adaptive or robust stabilization
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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References:

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