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Global Mittag–Leffler stability of complex valued fractional-order neural network with discrete and distributed delays

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Abstract

Fractional-order Hopfield neural network are often used to model the processing of information on the basis of interaction among the neurons. To show the constancy of the processed information, the system needs to be stable. In this paper, we deal with the problem of existence and uniform stability analysis of a complex valued fractional order delayed neural network. Moreover, as an extension to real valued neural network, this paper provides sufficient conditions for Mittag–Leffler stability of the system. At the end, we give three suitable examples to substantiate the effectiveness of the obtained theoretical results.

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Acknowledgments

We are thankful to the reviewers for their constructive comments and suggestions, which helped in improving the manuscript considerably.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology, Mandi, HP, 175001, India

    Swati Tyagi & Syed Abbas

  2. Laboratory of Applied Mathematics, Biskra University, PO. Box 145, 07000, Biskra, Algeria

    Mokhtar Hafayed

Authors
  1. Swati Tyagi
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  2. Syed Abbas
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  3. Mokhtar Hafayed
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Correspondence to Syed Abbas.

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Tyagi, S., Abbas, S. & Hafayed, M. Global Mittag–Leffler stability of complex valued fractional-order neural network with discrete and distributed delays. Rend. Circ. Mat. Palermo, II. Ser 65, 485–505 (2016). https://doi.org/10.1007/s12215-016-0248-8

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  • DOI: https://doi.org/10.1007/s12215-016-0248-8

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