Generalized synchronization in complex dynamical networks via adaptive couplings

Hui Liu, Juan Chen, Jun-an Lu and Ming Cao

Physica A: Statistical Mechanics and its Applications, 2010, vol. 389, issue 8, 1759-1770

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.

Keywords: Complex dynamical network; Generalized synchronization; Adaptive coupling strength; Heterogeneity (search for similar items in EconPapers)
Date: 2010
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:389:y:2010:i:8:p:1759-1770

DOI: 10.1016/j.physa.2009.12.035

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