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Exponential synchronization of a class of chaotic neural networks

Author

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  • Cheng, Chao-Jung
  • Liao, Teh-Lu
  • Hwang, Chi-Chuan

Abstract

This paper deals with the synchronization problem of a class of chaotic neural networks with or without delays. This class of chaotic neural networks covers several well-known neural networks, such as Hopfield neural networks, cellular neural networks, and bidirectional associative memory networks with or without delays. Using the drive-response concept, a control law is derived to achieve the state synchronization of two identical chaotic neural networks. Furthermore, based on the Lyapunov stability method and the Halanay inequality lemma, a delay independent sufficient exponential synchronization condition is derived. The synchronization condition is easy to verify and relies on the connection matrix in the driven networks and the suitable designed controller gain matrix in the response networks. Finally, some illustrative examples are given to demonstrate the effectiveness of the presented synchronization scheme.

Suggested Citation

  • Cheng, Chao-Jung & Liao, Teh-Lu & Hwang, Chi-Chuan, 2005. "Exponential synchronization of a class of chaotic neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 197-206.
    • Handle: RePEc:eee:chsofr:v:24:y:2005:i:1:p:197-206
    DOI: 10.1016/j.chaos.2004.09.022
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    Cited by:

    1. Park, Ju H., 2007. "An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 800-807.
    2. Park, Ju H., 2008. "On global stability criterion of neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 444-449.
    3. Xiong, Wenjun & Xie, Wei & Cao, Jinde, 2006. "Adaptive exponential synchronization of delayed chaotic networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(2), pages 832-842.
    4. Lu, Hongtao & van Leeuwen, C., 2006. "Synchronization of chaotic neural networks via output or state coupling," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 166-176.
    5. Zhang, Hongmei & Cao, Jinde & Xiong, Lianglin, 2019. "Novel synchronization conditions for time-varying delayed Lur’e system with parametric uncertainty," Applied Mathematics and Computation, Elsevier, vol. 350(C), pages 224-236.
    6. Zhu, Wei & Xu, Daoyi & Huang, Yumei, 2008. "Global impulsive exponential synchronization of time-delayed coupled chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(5), pages 904-912.
    7. Park, Ju H. & Kwon, O.M., 2009. "Global stability for neural networks of neutral-type with interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1174-1181.
    8. Gui, Zhanji & Ge, Weigao, 2007. "Periodic solutions of nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1760-1771.
    9. Jiang, Yanhong & Yang, Bin & Wang, Jincheng & Shao, Cheng, 2009. "Delay-dependent stability criterion for delayed Hopfield neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2133-2137.
    10. Wang, Weiping & Jia, Xiao & Luo, Xiong & Kurths, Jürgen & Yuan, Manman, 2019. "Fixed-time synchronization control of memristive MAM neural networks with mixed delays and application in chaotic secure communication," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 85-96.
    11. Park, Ju H., 2006. "On global stability criterion for neural networks with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(4), pages 897-902.
    12. Li, Tao & Fei, Shu-min & Zhang, Kan-jian, 2008. "Synchronization control of recurrent neural networks with distributed delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(4), pages 982-996.
    13. Gu, Ya-Qin & Shao, Chun & Fu, Xin-Chu, 2006. "Complete synchronization and stability of star-shaped complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 480-488.
    14. Lu, Junwei & Guo, Yiqian & Xu, Shengyuan, 2006. "Global asymptotic stability analysis for cellular neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 349-353.
    15. Qu, Hong & Yi, Zhang, 2007. "A new algorithm for finding the shortest paths using PCNNs," Chaos, Solitons & Fractals, Elsevier, vol. 33(4), pages 1220-1229.
    16. Lou, Xuyang & Cui, Baotong, 2007. "Synchronization of competitive neural networks with different time scales," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 563-576.
    17. Song, Qiankun & Cao, Jinde, 2007. "Synchronization and anti-synchronization for chaotic systems," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 929-939.
    18. Lu, Jianquan & Cao, Jinde, 2007. "Synchronization-based approach for parameters identification in delayed chaotic neural networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(2), pages 672-682.
    19. Hu, Jiming, 2009. "Synchronization conditions for chaotic nonlinear continuous neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2495-2501.

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