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Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays

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Abstract

In this paper, we study the hybrid projective synchronization problem for a class of fractional-order memristor-based neural networks with time delays. First, we address the basic ideas of fractional-order memristor-based neural networks (FMNNs) with hub structure and time delays. After that we derive the response system can be synchronized from the corresponding drive system, that is, the response system can be synchronized with the projection of the drive system generated through a design scaling matrix which is known as hybrid projective synchronization. By applying the Filippovs solutions, differential inclusion theory, stability theorem of linear fractional-order systems with multiple time delays and employing suitable linear feedback control law, some new sufficient conditions are derived to guaranteeing the projective synchronization of addressed FMNNs with hub structure and time delays. The analysis in this paper is based on the theory of fractional-order differential equations with discontinuous right-hand sides. Finally, a numerical example is presented to show the usefulness of our theoretical results.

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Authors and Affiliations

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

    G. Velmurugan & R. Rakkiyappan

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  1. G. Velmurugan
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  2. R. Rakkiyappan
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Correspondence to R. Rakkiyappan.

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The work was supported by CSIR Research Project No. 25(0237)/14/EMR-II.

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Velmurugan, G., Rakkiyappan, R. Hybrid projective synchronization of fractional-order memristor-based neural networks with time delays. Nonlinear Dyn 83, 419–432 (2016). https://doi.org/10.1007/s11071-015-2337-1

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