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Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses

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Abstract

The finite-time Mittag-Leffler stability for fractional-order quaternion-valued memristive neural networks (FQMNNs) with impulsive effect is studied here. A new mathematical expression of the quaternion-value memductance (memristance) is proposed according to the feature of the quaternion-valued memristive and a new class of FQMNNs is designed. In quaternion field, by using the framework of Filippov solutions as well as differential inclusion theoretical analysis, suitable Lyapunov-functional and some fractional inequality techniques, the existence of unique equilibrium point and Mittag-Leffler stability in finite time analysis for considered impulsive FQMNNs have been established with the order \(0<\beta <1\). Then, for the fractional order \(\beta \) satisfying \(1<\beta <2\) and by ignoring the impulsive effects, a new sufficient criterion are given to ensure the finite time stability of considered new FQMNNs system by the employment of Laplace transform, Mittag-Leffler function and generalized Gronwall inequality. Furthermore, the asymptotic stability of such system with order \(1<\beta <2\) have been investigated. Ultimately, the accuracy and validity of obtained finite time stability criteria are supported by two numerical examples.

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Authors and Affiliations

  1. Vel Tech High Tech Dr Rangarajan Dr Sakunthala Engineering College, Chennai, 600 062, India

    A. Pratap & J. Dianavinnarasi

  2. Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi, 630 004, India

    R. Raja

  3. Department of Mathematics and General Sciences, Prince Sultan University, Riyadh, 12435, Saudi Arabia

    J. Alzabut

  4. School of Mathematics, Southeast University, Nanjing, 211189, China

    J. Cao

  5. Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai, Thailand

    G. Rajchakit

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  1. A. Pratap
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Correspondence to J. Cao.

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Pratap, A., Raja, R., Alzabut, J. et al. Finite-Time Mittag-Leffler Stability of Fractional-Order Quaternion-Valued Memristive Neural Networks with Impulses. Neural Process Lett 51, 1485–1526 (2020). https://doi.org/10.1007/s11063-019-10154-1

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