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Dynamic analysis for high-order Hopfield neural networks with leakage delay and impulsive effects

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Abstract

This paper considers existence, uniqueness, and the global asymptotic stability for a class of High-order Hopfield neural networks with mixed delays and impulses. The mixed delays include constant delay in the leakage term (i.e., "leakage delay") and time-varying delays. Based on the Lyapunov stability theory, together with the linear matrix inequality approach and free-weighting matrix method, some less conservative delay-dependent sufficient conditions are presented for the global asymptotic stability of the equilibrium point of the considered neural networks. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the applicability of the result.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore, 641046, Tamilnadu, India

    R. Rakkiyappan

  2. Department of Science and Humanities, Sri Ramakrishna Institute of Technology, Pachapalayam, Coimbatore, 641010, Tamilnadu, India

    C. Pradeep

  3. Department of Mathematics and Computer Applications, P.S.G College of Technology, Coimbatore, 641004, Tamilnadu, India

    A. Vinodkumar

  4. Department of Mathematics, Faculty of Science, UAE University, Al-Ain, 17551, UAE

    Fathalla A. Rihan

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  1. R. Rakkiyappan
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  2. C. Pradeep
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  3. A. Vinodkumar
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  4. Fathalla A. Rihan
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Correspondence to R. Rakkiyappan.

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Rakkiyappan, R., Pradeep, C., Vinodkumar, A. et al. Dynamic analysis for high-order Hopfield neural networks with leakage delay and impulsive effects. Neural Comput & Applic 22 (Suppl 1), 55–73 (2013). https://doi.org/10.1007/s00521-012-0997-z

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  • DOI: https://doi.org/10.1007/s00521-012-0997-z

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