IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v37y2008i3p799-806.html
   My bibliography  Save this article

Transition to chaos in small-world dynamical network

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077906009271
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2006.09.077?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lu, Jianquan & Ho, Daniel W.C., 2008. "Local and global synchronization in general complex dynamical networks with delay coupling," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1497-1510.
    2. Guan, Zhi-Hong & Zhang, Hao, 2008. "Stabilization of complex network with hybrid impulsive and switching control," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1372-1382.
    3. Vinayak, & Raghuvanshi, Adarsh & kshitij, Avinash, 2023. "Signatures of capacity development through research collaborations in artificial intelligence and machine learning," Journal of Informetrics, Elsevier, vol. 17(1).
    4. Wang, Weiwei & Cao, Jinde, 2006. "Synchronization in an array of linearly coupled networks with time-varying delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 197-211.
    5. Lahtinen, Jani & Kertész, János & Kaski, Kimmo, 2005. "Sandpiles on Watts–Strogatz type small-worlds," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 349(3), pages 535-547.
    6. Liu, Run-Ran & Chu, Changchang & Meng, Fanyuan, 2023. "Higher-order interdependent percolation on hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
    7. Li, Fengbing & Ma, Zhongjun & Duan, Qichang, 2019. "Partial component synchronization on chaotic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 707-714.
    8. Lee Fleming & Charles King & Adam I. Juda, 2007. "Small Worlds and Regional Innovation," Organization Science, INFORMS, vol. 18(6), pages 938-954, December.
    9. J. H. Park & S. M. Lee & H. Y. Jung, 2009. "LMI Optimization Approach to Synchronization of Stochastic Delayed Discrete-Time Complex Networks," Journal of Optimization Theory and Applications, Springer, vol. 143(2), pages 357-367, November.
    10. Dorso, Claudio O. & Medus, Andrés & Balenzuela, Pablo, 2017. "Vaccination and public trust: A model for the dissemination of vaccination behaviour with external intervention," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 482(C), pages 433-443.
    11. Wu, Jianshe & Jiao, Licheng, 2008. "Synchronization in dynamic networks with nonsymmetrical time-delay coupling based on linear feedback controllers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(8), pages 2111-2119.
    12. Marjan Sedighi Anaraki & Fangyan Dong & Hajime Nobuhara & Kaoru Hirota, 2006. "Visualization of Complex Networks Based on Dyadic Curvelet Transform," Interdisciplinary Description of Complex Systems - scientific journal, Croatian Interdisciplinary Society Provider Homepage: http://indecs.eu, vol. 4(1), pages 51-62.
    13. Xenikos, D.G. & Constantoudis, V., 2023. "Weibull dynamics and power-law diffusion of epidemics in small world 2D networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 617(C).
    14. Floortje Alkemade & Carolina Castaldi, 2005. "Strategies for the Diffusion of Innovations on Social Networks," Computational Economics, Springer;Society for Computational Economics, vol. 25(1), pages 3-23, February.
    15. Huo, Liang’an & Song, Naixiang, 2016. "Dynamical interplay between the dissemination of scientific knowledge and rumor spreading in emergency," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 73-84.
    16. Mark Newman, 1999. "Small Worlds: The Structure of Social Networks," Working Papers 99-12-080, Santa Fe Institute.
    17. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Global synchronization in general complex delayed dynamical networks and its applications," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 385(2), pages 729-742.
    18. Li, Fengbing & Ma, Zhongjun & Duan, Qichang, 2019. "Clustering component synchronization in a class of unconnected networks via pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 394-401.
    19. Shen, Ai-Zhong & Guo, Jin-Li & Wu, Guo-Lin & Jia, Shu-Wei, 2018. "The agglomeration phenomenon influence on the scaling law of the scientific collaboration system," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 461-467.
    20. I. Vieira & R. Cheng & P. Harper & V. Senna, 2010. "Small world network models of the dynamics of HIV infection," Annals of Operations Research, Springer, vol. 178(1), pages 173-200, July.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:chsofr:v:37:y:2008:i:3:p:799-806. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.