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Global exponential stability of Cohen–Grossberg neural networks with time-varying delays

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  • Liu, Jiang

Abstract

The global exponential stability of the equilibrium point of Cohen–Grossberg neural networks with time-varying delays is first investigated. Furthermore, some sufficient conditions for existence and uniqueness of equilibrium and global exponential stability of the time-varying delayed Cohen–Grossberg neural networks are obtained by using the topological degree theory, M-matrix, Lyapunov functional method and some analysis techniques.

Suggested Citation

  • Liu, Jiang, 2005. "Global exponential stability of Cohen–Grossberg neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 935-945.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:3:p:935-945
    DOI: 10.1016/j.chaos.2005.01.062
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    Cited by:

    1. Sun, Yeong-Jeu & Gau, Ruey-Shyan & Hsieh, Jer-Guang, 2009. "Simple criteria for sector root clustering of uncertain systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 65-71.
    2. Sun, Yeong-Jeu, 2007. "Stability criterion for a class of descriptor systems with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 986-993.
    3. Li, Chun-Hsien & Yang, Suh-Yuh, 2009. "Existence and attractivity of periodic solutions to non-autonomous Cohen–Grossberg neural networks with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1235-1244.
    4. Sun, Yeong-Jeu, 2007. "Duality between observation and output feedback for linear systems with multiple time delays," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 879-884.
    5. Ping, Zhao Wu & Lu, Jun Guo, 2009. "Global exponential stability of impulsive Cohen–Grossberg neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 164-174.
    6. Wen, Zhen & Sun, Jitao, 2009. "Stability analysis of delayed Cohen–Grossberg BAM neural networks with impulses via nonsmooth analysis," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1829-1837.
    7. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Exponential p-stability of delayed Cohen–Grossberg-type BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 806-818.
    8. Bing Li & Yongkun Li, 2019. "Existence and Global Exponential Stability of Almost Automorphic Solution for Clifford-Valued High-Order Hopfield Neural Networks with Leakage Delays," Complexity, Hindawi, vol. 2019, pages 1-13, July.
    9. Sun, Jitao & Wang, Qing-Guo & Gao, Hanqiao, 2009. "Periodic solution for nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1423-1427.
    10. Li, Chun-Hsien & Yang, Suh-Yuh, 2007. "A further analysis on harmless delays in Cohen–Grossberg neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 646-653.
    11. Zeng, Xu & Li, Chuandong & Huang, Tingwen & He, Xing, 2015. "Stability analysis of complex-valued impulsive systems with time delay," Applied Mathematics and Computation, Elsevier, vol. 256(C), pages 75-82.
    12. Lu Pang & Cheng Hu & Juan Yu & Haijun Jiang, 2022. "Fixed-Time Synchronization for Fuzzy-Based Impulsive Complex Networks," Mathematics, MDPI, vol. 10(9), pages 1-16, May.
    13. Liu, Bingwen & Huang, Lihong, 2007. "Existence and exponential stability of almost periodic solutions for cellular neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 95-103.
    14. Sun, Yeong-Jeu, 2009. "Stability criteria for a class of differential inclusion systems with discrete and distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(5), pages 2386-2391.
    15. Mohamad, Sannay, 2008. "Computer simulations of exponentially convergent networks with large impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 77(4), pages 331-344.
    16. Liu, Hailin & Chen, Guohua, 2007. "Delay-dependent stability for neural networks with time-varying delay," Chaos, Solitons & Fractals, Elsevier, vol. 33(1), pages 171-177.
    17. Liu, Bingwen, 2007. "Almost periodic solutions for Hopfield neural networks with continuously distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 73(5), pages 327-335.
    18. Zhao, Weirui & Zhang, Huanshui, 2009. "New results of almost periodic solutions for cellular neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 831-838.
    19. Huang, Tingwen & Li, Chuandong & Chen, Goong, 2007. "Stability of Cohen–Grossberg neural networks with unbounded distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 992-996.
    20. Chen, Ling & Zhao, Hongyong, 2008. "Global stability of almost periodic solution of shunting inhibitory cellular neural networks with variable coefficients," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 351-357.

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