Generalized synchronization in complex dynamical networks via adaptive couplings |
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Authors: | Hui Liu Juan Chen |
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Affiliation: | a School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China b Faculty of Mathematics and Natural Sciences, ITM, University of Groningen, Groningen, 9747 AG, The Netherlands |
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Abstract: | This paper investigates generalized synchronization of three typical classes of complex dynamical networks: scale-free networks, small-world networks, and interpolating networks. The proposed synchronization strategy is to adjust adaptively a node’s coupling strength based on the node’s local generalized synchronization information. By taking the auxiliary-system approach and using the Lyapunov function method, we prove that for any given initial coupling strengths, the generalized synchronization can take place in complex networks consisting of nonidentical dynamical systems. It is demonstrated that the coupling strengths are affected by topologies of the networks. Furthermore, it is found that there are hierarchical features in the processes of generalized synchronization in scale-free networks because of their highly heterogeneous distributions of connection degree. Finally, we discuss in detail how a network’s degree of heterogeneity affects its generalization synchronization behavior. |
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Keywords: | Complex dynamical network Generalized synchronization Adaptive coupling strength Heterogeneity |
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