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Stability analysis of memristor-based fractional-order neural networks with different memductance functions

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Abstract

In this paper, the problem of the existence, uniqueness and uniform stability of memristor-based fractional-order neural networks (MFNNs) with two different types of memductance functions is extensively investigated. Moreover, we formulate the complex-valued memristor-based fractional-order neural networks (CVMFNNs) with two different types of memductance functions and analyze the existence, uniqueness and uniform stability of such networks. By using Banach contraction principle and analysis technique, some sufficient conditions are obtained to ensure the existence, uniqueness and uniform stability of the considered MFNNs and CVMFNNs with two different types of memductance functions. The analysis results establish from the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, four numerical examples are presented to show the effectiveness of our theoretical results.

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Acknowledgments

This work was supported by NBHM research Project No. 2/48(7)/2012/NBHM(R.P.)/R and D-II/12669, the National Natural Science Foundation of China under Grant Nos. 61272530 and 11072059, the Natural Science Foundation of Jiangsu Province of China under Grant No. BK2012741, and the Specialized Research Fund for the Doctoral Program of Higher Education under Grant Nos. 20110092110017 and 20130092110017.

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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, and 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

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  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.

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Rakkiyappan, R., Velmurugan, G. & Cao, J. Stability analysis of memristor-based fractional-order neural networks with different memductance functions. Cogn Neurodyn 9, 145–177 (2015). https://doi.org/10.1007/s11571-014-9312-2

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  • DOI: https://doi.org/10.1007/s11571-014-9312-2

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