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Adaptive Synchronization of Complex Dynamical Multilinks Networks with Similar Nodes

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  • Weiping Wang
  • Lixiang Li
  • Haipeng Peng
  • Jialiang Yuan
  • Jinghua Xiao
  • Yixian Yang

Abstract

This paper studies the synchronization of complex dynamical networks with multilinks and similar nodes. The dynamics of all the nodes in the networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations. Networks with similar nodes are universal in the real world. In order to depict the similarity of the similar nodes, we give the definition of the minimal similarity of the nodes in the network for the first time. We find the threshold of the minimal similarity of the nodes in the network. If the minimal similarity of the nodes is bigger than the threshold, then the similar nodes can achieve synchronization without controllers. Otherwise, adaptive synchronization method is adopted to synchronize similar nodes in the network. Some new synchronization criteria are proposed based on the Lyapunov stability theory. Finally, numerical simulations are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.

Suggested Citation

  • Weiping Wang & Lixiang Li & Haipeng Peng & Jialiang Yuan & Jinghua Xiao & Yixian Yang, 2013. "Adaptive Synchronization of Complex Dynamical Multilinks Networks with Similar Nodes," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-12, June.
    • Handle: RePEc:hin:jnlmpe:736585
    DOI: 10.1155/2013/736585
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    Cited by:

    1. Yadav, Vijay K. & Shukla, Vijay K. & Das, Subir, 2021. "Exponential synchronization of fractional-order complex chaotic systems and its application," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    2. Sun, Yanqin & Wu, Huaiyu & Chen, Zhihuan & Zheng, Xiujuan & Chen, Yang, 2021. "Outer synchronization of two different multi-links complex networks by chattering-free control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 584(C).

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