IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v381y2007icp82-92.html
   My bibliography  Save this article

Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling

Author

Listed:
  • Liu, Xiwei
  • Chen, Tianping

Abstract

In this paper, we discuss exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling. Sufficient conditions for both delay-independent and delay-dependent global exponential synchronization are obtained based on Lyapunov functional method. It is shown that, for some coupled chaotic systems and nonlinear coupling functions, if the coupling delay is less than a positive threshold, then the coupled network will be synchronized. On the other hand, with the increase of coupling delay, the synchronizability of the coupled network will be restrained, even eventually de-synchronized. Finally, an example is provided to demonstrate the effectiveness of the proposed results.

Suggested Citation

  • Liu, Xiwei & Chen, Tianping, 2007. "Exponential synchronization of nonlinear coupled dynamical networks with a delayed coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 82-92.
    • Handle: RePEc:eee:phsmap:v:381:y:2007:i:c:p:82-92
    DOI: 10.1016/j.physa.2007.03.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437107002646
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2007.03.026?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. Lind, Pedro G. & Nunes, Ana & Gallas, Jason A.C., 2006. "Impact of bistability in the synchronization of chaotic maps with delayed coupling and complex topologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 371(1), pages 100-103.
    2. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    3. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
    4. Vasconcelos, D.B. & Viana, R.L. & Lopes, S.R. & Batista, A.M. & Pinto, S.E. de S., 2004. "Spatial correlations and synchronization in coupled map lattices with long-range interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 201-218.
    5. Li, Chunguang & Li, Shaowen & Liao, Xiaofeng & Yu, Juebang, 2004. "Synchronization in coupled map lattices with small-world delayed interactions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 335(3), pages 365-370.
    6. 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.
    7. Yun Wang, Qing & Rong Chen, Guan & Shao Lu, Qi & Hao, Fei, 2007. "Novel criteria of synchronization stability in complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 527-536.
    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. Suo, JingJing & Hu, Hongxiao & Xu, Liguang, 2023. "Delay-dependent impulsive control for lag quasi-synchronization of stochastic complex dynamical networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 211(C), pages 134-153.
    2. Hongjie Li & W. K. Wong & Yang Tang, 2012. "Global Synchronization Stability for Stochastic Complex Dynamical Networks with Probabilistic Interval Time-Varying Delays," Journal of Optimization Theory and Applications, Springer, vol. 152(2), pages 496-516, February.
    3. Liu, Xiwei & Chen, Tianping, 2008. "Synchronization analysis for nonlinearly-coupled complex networks with an asymmetrical coupling matrix," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4429-4439.
    4. Tseng, Jui-Pin, 2016. "A novel approach to synchronization of nonlinearly coupled network systems with delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 452(C), pages 266-280.
    5. Lu, Jun Guo & Chen, Guanrong, 2009. "Global asymptotical synchronization of chaotic neural networks by output feedback impulsive control: An LMI approach," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2293-2300.
    6. Junwei Wang & Kairui Chen & Yun Zhang, 2017. "Consensus of High-Order Nonlinear Multiagent Systems with Constrained Switching Topologies," Complexity, Hindawi, vol. 2017, pages 1-11, January.
    7. Korneev, I.A. & Semenov, V.V. & Slepnev, A.V. & Vadivasova, T.E., 2021. "Complete synchronization of chaos in systems with nonlinear inertial coupling," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).

    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. 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.
    2. Wang, Qingyun & Duan, Zhisheng & Chen, Guanrong & Feng, Zhaosheng, 2008. "Synchronization in a class of weighted complex networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5616-5622.
    3. Liu, Tao & Dimirovski, Georgi M. & Zhao, Jun, 2008. "Exponential synchronization of complex delayed dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 643-652.
    4. 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.
    5. He, Guangming & Yang, Jingyu, 2008. "Adaptive synchronization in nonlinearly coupled dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(5), pages 1254-1259.
    6. Yang, Yong & Tu, Lilan & Li, Kuanyang & Guo, Tianjiao, 2019. "Optimized inter-structure for enhancing the synchronizability of interdependent networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 521(C), pages 310-318.
    7. Wu, Jianshe & Jiao, Licheng, 2007. "Synchronization in complex delayed dynamical networks with nonsymmetric coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 513-530.
    8. Du, Hongyue, 2011. "Function projective synchronization in drive–response dynamical networks with non-identical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 44(7), pages 510-514.
    9. 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.
    10. Wu, Jianshe & Jiao, Licheng, 2007. "Observer-based synchronization in complex dynamical networks with nonsymmetric coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 469-480.
    11. Liu, Tao & Zhao, Jun & Hill, David J., 2009. "Synchronization of complex delayed dynamical networks with nonlinearly coupled nodes," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1506-1519.
    12. 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.
    13. L. Jarina Banu & P. Balasubramaniam, 2014. "Synchronisation of discrete-time complex networks with randomly occurring uncertainties, nonlinearities and time-delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 45(7), pages 1427-1450, July.
    14. 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.
    15. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
    16. Fei Wang & Zhaowen Zheng & Yongqing Yang, 2019. "Synchronization of Complex Dynamical Networks with Hybrid Time Delay under Event-Triggered Control: The Threshold Function Method," Complexity, Hindawi, vol. 2019, pages 1-17, December.
    17. Lei, Lixing & Yang, Junzhong, 2021. "Patterns in coupled FitzHugh–Nagumo model on duplex networks," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    18. Zhang, Chuan & Wang, Xingyuan & Luo, Chao & Li, Junqiu & Wang, Chunpeng, 2018. "Robust outer synchronization between two nonlinear complex networks with parametric disturbances and mixed time-varying delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 494(C), pages 251-264.
    19. Zhang, Hai & Ye, Miaolin & Ye, Renyu & Cao, Jinde, 2018. "Synchronization stability of Riemann–Liouville fractional delay-coupled complex neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 155-165.
    20. Yang, Li-xin & Jiang, Jun, 2018. "Synchronization analysis of fractional order drive-response networks with in-commensurate orders," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 47-52.

    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:phsmap:v:381:y:2007:i:c:p:82-92. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.