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Stability in impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays: A general analysis

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  • Li, Kelin
  • Zeng, Huanglin

Abstract

In this paper, we investigate a class of impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays. By establishing the delay differential inequality with impulsive initial conditions, and employing the homeomorphism theory, the M-matrix theory and the inequality a∏k=1lbkqk≤(1/r)(ar+∑k=1lqkbkr) (a≥0,bk≥0,qk≥0 with ∑k=1lqk=r−1, and r≥1), some new sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays are derived. In particular, the estimate of the exponential convergence rate which depends on the system parameters and the impulsive disturbance intension is also provided. An example is given to show the effectiveness of the results obtained here.

Suggested Citation

  • Li, Kelin & Zeng, Huanglin, 2010. "Stability in impulsive Cohen–Grossberg-type BAM neural networks with time-varying delays: A general analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(12), pages 2329-2349.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:12:p:2329-2349
    DOI: 10.1016/j.matcom.2010.05.012
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    References listed on IDEAS

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    1. 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.
    2. Bai, Chuanzhi, 2008. "Stability analysis of Cohen–Grossberg BAM neural networks with delays and impulses," Chaos, Solitons & Fractals, Elsevier, vol. 35(2), pages 263-267.
    3. Huang, Zhenkun & Xia, Yonghui, 2008. "Global exponential stability of BAM neural networks with transmission delays and nonlinear impulses," Chaos, Solitons & Fractals, Elsevier, vol. 38(2), pages 489-498.
    4. 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.
    5. Xia, Yonghui & Huang, Zhenkun & Han, Maoan, 2008. "Existence and globally exponential stability of equilibrium for BAM neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 588-597.
    6. Chen, Jun & Cui, Baotong, 2008. "Impulsive effects on global asymptotic stability of delay BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1115-1125.
    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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