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Exponential stability in Hopfield-type neural networks with impulses

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  • Mohamad, Sannay

Abstract

This paper demonstrates that there is an exponentially stable unique equilibrium state in a Hopfield-type neural network that is subject to quite large impulses that are not too frequent. The activation functions are assumed to be globally Lipschitz continuous and unbounded. The analysis exploits an homeomorphic mapping and an appropriate Lyapunov function, and also either a geometric–arithmetic mean inequality or a Young inequality, to derive a family of easily verifiable sufficient conditions for convergence to the unique globally stable equilibrium state. These sufficiency conditions, in the norm ∥·∥p where p⩾1, include those governing the network parameters and the impulse magnitude and frequency.

Suggested Citation

  • Mohamad, Sannay, 2007. "Exponential stability in Hopfield-type neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 32(2), pages 456-467.
    • Handle: RePEc:eee:chsofr:v:32:y:2007:i:2:p:456-467
    DOI: 10.1016/j.chaos.2006.06.035
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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.
    2. 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. Xu, Bingji & Xu, Yuan & He, Linman, 2012. "LMI-based stability analysis of impulsive high-order Hopfield-type neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 86(C), pages 67-77.
    2. 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.
    3. Luo, Wenpin & Zhong, Shouming & Yang, Jun, 2009. "Global exponential stability of impulsive Cohen–Grossberg neural networks with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1084-1091.
    4. Xu, Liguang & Xu, Daoyi, 2009. "Exponential p-stability of impulsive stochastic neural networks with mixed delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 263-272.
    5. Zhang, Yinping, 2009. "Stationary oscillation for nonautonomous bidirectional associative memory neural networks with impulse," Chaos, Solitons & Fractals, Elsevier, vol. 41(4), pages 1760-1763.
    6. He, Zhilong & Li, Chuandong & Li, Hongfei & Zhang, Qiangqiang, 2020. "Global exponential stability of high-order Hopfield neural networks with state-dependent impulses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    7. 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.
    8. 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.

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