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A new stability criterion for discrete-time neural networks: Nonlinear spectral radius

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  • Mak, K.L.
  • Peng, J.G.
  • Xu, Z.B.
  • Yiu, K.F.C.

Abstract

In this paper, the exponential stability of nonlinear discrete-time systems is studied. A novel notion of nonlinear spectral radius is defined. Under the assumption of Lipschitz continuity for the activation function, the developed approach is applied to stability analysis of discrete-time neural networks. A series of sufficient conditions for global exponential stability of the neural networks are established and an estimate of the exponential decay rate is also derived for each case.

Suggested Citation

  • Mak, K.L. & Peng, J.G. & Xu, Z.B. & Yiu, K.F.C., 2007. "A new stability criterion for discrete-time neural networks: Nonlinear spectral radius," Chaos, Solitons & Fractals, Elsevier, vol. 31(2), pages 424-436.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:2:p:424-436
    DOI: 10.1016/j.chaos.2005.09.075
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    References listed on IDEAS

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    1. Arik, Sabri, 2005. "Global robust stability analysis of neural networks with discrete time delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1407-1414.
    2. He, Yong & Wang, Qing-Guo & Zheng, Wei-Xing, 2005. "Global robust stability for delayed neural networks with polytopic type uncertainties," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1349-1354.
    3. Yuan, Kun & Cao, Jinde, 2006. "Periodic oscillatory solution in delayed competitive–cooperative neural networks: A decomposition approach," Chaos, Solitons & Fractals, Elsevier, vol. 27(1), pages 223-231.
    4. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2005. "New stability conditions for neural networks with constant and variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(5), pages 1391-1398.
    5. 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. Shih, Chih-Wen & Tseng, Jui-Pin, 2009. "Global consensus for discrete-time competitive systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 302-310.
    2. Cheng, Sui Sun & Chen, Jhien-Shien & Yueh, Wen-Chyuan, 2009. "Cycles of a discrete time bipolar artificial neural network," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1319-1332.
    3. Avlant Nilsson & Joshua M. Peters & Nikolaos Meimetis & Bryan Bryson & Douglas A. Lauffenburger, 2022. "Artificial neural networks enable genome-scale simulations of intracellular signaling," Nature Communications, Nature, vol. 13(1), pages 1-16, December.

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