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Nonlinear fractional distributed Halanay inequality and application to neural network systems

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  • Kassim, Mohammed D.
  • Tatar, Nasser-eddine

Abstract

The standard first order distributed Halanay inequality is generalized in more than one direction. We prove a fractional nonlinear version of this inequality for a large class of kernels which are not necessarily exponentially decaying to zero. This result is used to prove Mittag-Leffler stability of a Hopfiled neural network system with not necessarily globally Lipschitz continuous activation functions. Two classes of important admissible kernels and an example are provided to illustrate our findings.

Suggested Citation

  • Kassim, Mohammed D. & Tatar, Nasser-eddine, 2021. "Nonlinear fractional distributed Halanay inequality and application to neural network systems," Chaos, Solitons & Fractals, Elsevier, vol. 150(C).
    • Handle: RePEc:eee:chsofr:v:150:y:2021:i:c:s0960077921004847
    DOI: 10.1016/j.chaos.2021.111130
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    References listed on IDEAS

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    1. Shuo Zhang & Yongguang Yu & Wei Hu, 2014. "Robust Stability Analysis of Fractional-Order Hopfield Neural Networks with Parameter Uncertainties," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-14, April.
    2. H. J. Haubold & A. M. Mathai & R. K. Saxena, 2011. "Mittag-Leffler Functions and Their Applications," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-51, May.
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    Cited by:

    1. Leng, Xiangxin & Wang, Xiaoping & Zeng, Zhigang, 2024. "Memristive Hopfield neural network with multiple controllable nonlinear offset behaviors and its medical encryption application," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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