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Global asymptotic stability of nonautonomous Cohen–Grossberg neural network models with infinite delays

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  • Esteves, Salete
  • Oliveira, José J.

Abstract

For a general Cohen–Grossberg neural network model with potentially unbounded time-varying coefficients and infinite distributed delays, we give sufficient conditions for its global asymptotic stability. The model studied is general enough to include, as subclass, the most of famous neural network models such as Cohen–Grossberg, Hopfield, and bidirectional associative memory. Contrary to usual in the literature, in the proofs we do not use Lyapunov functionals. As illustrated, the results are applied to several concrete models studied in the literature and a comparison of results shows that our results give new global stability criteria for several neural network models and improve some earlier publications.

Suggested Citation

  • Esteves, Salete & Oliveira, José J., 2015. "Global asymptotic stability of nonautonomous Cohen–Grossberg neural network models with infinite delays," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 333-346.
    • Handle: RePEc:eee:apmaco:v:265:y:2015:i:c:p:333-346
    DOI: 10.1016/j.amc.2015.04.103
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    References listed on IDEAS

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    1. Jiang, Haijun & Teng, Zhidong, 2006. "Boundedness and global stability for nonautonomous recurrent neural networks with distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 83-93.
    2. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2009. "Global exponential stability for nonautonomous cellular neural networks with unbounded delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1144-1151.
    3. Zhang, Qiang & Wei, Xiaopeng & Xu, Jin, 2009. "Exponential stability for nonautonomous neural networks with variable delays," Chaos, Solitons & Fractals, Elsevier, vol. 39(3), pages 1152-1157.
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    Cited by:

    1. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2019. "Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 868-883.
    2. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    3. Zhang, Chuan-Ke & He, Yong & Jiang, Lin & Lin, Wen-Juan & Wu, Min, 2017. "Delay-dependent stability analysis of neural networks with time-varying delay: A generalized free-weighting-matrix approach," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 102-120.
    4. Balasundaram, K. & Raja, R. & Pratap, A. & Chandrasekaran, S., 2019. "Impulsive effects on competitive neural networks with mixed delays: Existence and exponential stability analysis," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 290-302.

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