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Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses

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  • Xia, Yonghui
  • Cao, Jinde
  • Huang, Zhenkun

Abstract

In this paper, by using the contraction principle and Gronwall–Bellman’s inequality, some sufficient conditions are obtained for checking the existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks (SICNNs) with impulse. Our results are essentially new. It is the first time that the existence of almost periodic solutions for the impulsive neural networks are obtained.

Suggested Citation

  • Xia, Yonghui & Cao, Jinde & Huang, Zhenkun, 2007. "Existence and exponential stability of almost periodic solution for shunting inhibitory cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 34(5), pages 1599-1607.
    • Handle: RePEc:eee:chsofr:v:34:y:2007:i:5:p:1599-1607
    DOI: 10.1016/j.chaos.2006.05.003
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    References listed on IDEAS

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    1. Li, Yongkun & Xing, Wenya & Lu, Linghong, 2006. "Existence and global exponential stability of periodic solution of a class of neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 437-445.
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    Cited by:

    1. Zhang, Huiying & Xia, Yonghui, 2008. "Existence and exponential stability of almost periodic solution for Hopfield-type neural networks with impulse," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 1076-1082.
    2. Kashkynbayev, Ardak & Cao, Jinde & Suragan, Durvudkhan, 2021. "Global Lagrange stability analysis of retarded SICNNs," Chaos, Solitons & Fractals, Elsevier, vol. 145(C).
    3. Xia, Yonghui & Wong, Patricia J.Y., 2009. "Global exponential stability of a class of retarded impulsive differential equations with applications," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 440-453.
    4. Huang, Zaitang & Yang, Qi-Gui, 2009. "Existence and exponential stability of almost periodic solution for stochastic cellular neural networks with delay," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 773-780.
    5. Ninghua Chen, 2013. "Existence of Periodic Solutions for Shunting Inhibitory Cellular Neural Networks with Neutral Delays," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-8, October.
    6. Yu, Jiali & Yi, Zhang & Zhang, Lei, 2009. "Periodicity of a class of nonlinear fuzzy systems with delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1343-1351.
    7. Sun, Yeong-Jeu, 2009. "Global exponential stability criterion for uncertain discrete-time cellular neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 2022-2024.
    8. Zhao, Weirui, 2009. "On existence and global exponential stability of periodic solution of two-neuron networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1100-1105.
    9. Lan, Heng-you & Cui, Yi-Shun, 2009. "A neural network method for solving a system of linear variational inequalities," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1245-1252.
    10. Wang, Xiaohu & Xu, Daoyi, 2009. "Global exponential stability of impulsive fuzzy cellular neural networks with mixed delays and reaction-diffusion terms," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2713-2721.
    11. Huang, Zhenkun & Xia, Yonghui, 2009. "Exponential periodic attractor of impulsive BAM networks with finite distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 373-384.
    12. 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.
    13. Wang, Jiafu & Huang, Lihong, 2012. "Almost periodicity for a class of delayed Cohen–Grossberg neural networks with discontinuous activations," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1157-1170.
    14. 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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