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Transition to chaos in small-world dynamical network

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  • Yuan, Wu-Jie
  • Luo, Xiao-Shu
  • Jiang, Pin-Qun
  • Wang, Bing-Hong
  • Fang, Jin-Qing

Abstract

The transition from a non-chaotic state to a chaotic state is an important issue in the study of coupled dynamical networks. In this paper, by using the theoretical analysis and numerical simulation, we study the dynamical behaviors of the NW small-world dynamical network consisting of nodes that are in non-chaotic states before they are coupled together. It is found that, for any given coupling strength and a sufficiently large number of nodes, the small-world dynamical network can be chaotic, even if the nearest-neighbor coupled network cannot be chaotic under the same condition. More interesting, the numerical results show that the measurement 1R of the transition ability from non-chaos to chaos approximately obeys power-law forms as 1R∼p-r1 and 1R∼N-r2. Furthermore, based on dissipative system criteria, we obtain the relationship between the network topology parameters and the coupling strength when the network is stable in the sense of Lyapunov (i. s. L.).

Suggested Citation

  • Yuan, Wu-Jie & Luo, Xiao-Shu & Jiang, Pin-Qun & Wang, Bing-Hong & Fang, Jin-Qing, 2008. "Transition to chaos in small-world dynamical network," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 799-806.
    • Handle: RePEc:eee:chsofr:v:37:y:2008:i:3:p:799-806
    DOI: 10.1016/j.chaos.2006.09.077
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    1. M. E. J. Newman & D. J. Watts, 1999. "Scaling and Percolation in the Small-World Network Model," Working Papers 99-05-034, Santa Fe Institute.
    2. Zhang, Hai-Feng & Wu, Rui-Xin & Fu, Xin-Chu, 2006. "The emergence of chaos in complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 472-479.
    3. Yang, Huijie & Zhao, Fangcui & Wang, Binghong, 2006. "Collective chaos induced by structures of complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 544-556.
    4. Lü, Jinhu & Yu, Xinghuo & Chen, Guanrong, 2004. "Chaos synchronization of general complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 334(1), pages 281-302.
    5. Li, Xiang & Chen, Guanrong & Ko, King-Tim, 2004. "Transition to chaos in complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 367-378.
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    Cited by:

    1. Lai, Qiang & Xu, Guanghui & Pei, Huiqin, 2019. "Analysis and control of multiple attractors in Sprott B system," Chaos, Solitons & Fractals, Elsevier, vol. 123(C), pages 192-200.

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