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Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays

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Abstract

In this paper, the problem of finite-time stability of fractional-order complex-valued memristor-based neural networks (NNs) with time delays is extensively investigated. We first initiate the fractional-order complex-valued memristor-based NNs with the Caputo fractional derivatives. Using the theory of fractional-order differential equations with discontinuous right-hand sides, Laplace transforms, Mittag-Leffler functions and generalized Gronwall inequality, some new sufficient conditions are derived to guarantee the finite-time stability of the considered fractional-order complex-valued memristor-based NNs. In addition, some sufficient conditions are also obtained for the asymptotical stability of fractional-order complex-valued memristor-based NNs. Finally, a numerical example is presented to demonstrate the effectiveness of our theoretical results.

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Authors and Affiliations

  1. Department of Mathematics, Bharathiar University, Coimbatore , 641 046, Tamilnadu, India

    R. Rakkiyappan & G. Velmurugan

  2. Department of Mathematics, Research Center for Complex Systems and Network Sciences, Southeast University, Nanjing , 210096, Jiangsu, China

    Jinde Cao

  3. Department of Mathematics, Faculty of Science, King Abdulaziz University, Jeddah , 21589, Saudi Arabia

    Jinde Cao

Authors
  1. R. Rakkiyappan
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  2. G. Velmurugan
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  3. Jinde Cao
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Correspondence to Jinde Cao.

Additional information

The work was supported by the National Natural Science Foundation of China under Grant 61272530, the Natural Science Foundation of Jiangsu Province of China under Grant BK2012741, and NBHM research project No. 2/48(7)/2012/NBHM(R.P.)/R and D-II/12669.

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Rakkiyappan, R., Velmurugan, G. & Cao, J. Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays. Nonlinear Dyn 78, 2823–2836 (2014). https://doi.org/10.1007/s11071-014-1628-2

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  • DOI: https://doi.org/10.1007/s11071-014-1628-2

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