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Existence and global exponential stability of periodic solution of CNNs with impulses

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  • Li, Yongkun
  • Xing, Zhiwei

Abstract

Sufficient conditions are obtained for the existence and global exponential stability of a unique periodic solution of cellular neural networks with variable time delays and impulses by using Mawhin’s continuation theorem of coincidence degree and by means of a method based on delay differential inequality.

Suggested Citation

  • Li, Yongkun & Xing, Zhiwei, 2007. "Existence and global exponential stability of periodic solution of CNNs with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1686-1693.
    • Handle: RePEc:eee:chsofr:v:33:y:2007:i:5:p:1686-1693
    DOI: 10.1016/j.chaos.2006.03.041
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    References listed on IDEAS

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    1. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "On global exponential stability of nonautonomous delayed neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 965-970.
    2. 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.
    3. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2006. "Stability analysis for cellular neural networks with variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 28(2), pages 331-336.
    4. Li, Chuandong & Liao, Xiaofeng & Zhang, Rong & Prasad, Ashutosh, 2005. "Global robust exponential stability analysis for interval neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 25(3), pages 751-757.
    5. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "Delay-dependent exponential stability of cellular neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1363-1369.
    6. 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.
    7. Li, Yongkun, 2005. "Global exponential stability of BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 279-285.
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    Cited by:

    1. 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.
    2. Li, Dong & Yang, Dan & Wang, Hui & Zhang, Xiaohong & Wang, Shilong, 2009. "Asymptotical stability of multi-delayed cellular neural networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(2), pages 218-224.
    3. Zhang, Yinping, 2009. "Stationary oscillation for cellular neural networks with time delays and impulses," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(10), pages 3174-3178.
    4. Mustafa Şaylı & Enes Yılmaz, 2017. "Anti-periodic solutions for state-dependent impulsive recurrent neural networks with time-varying and continuously distributed delays," Annals of Operations Research, Springer, vol. 258(1), pages 159-185, November.
    5. 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.

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