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Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties

Author

Listed:
  • Pharunyou Chanthorn

    (Research Center in Mathematics and Applied Mathematics, Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, Thailand)

  • Grienggrai Rajchakit

    (Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 52290, Thailand)

  • Jenjira Thipcha

    (Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 52290, Thailand)

  • Chanikan Emharuethai

    (Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 52290, Thailand)

  • Ramalingam Sriraman

    (Department of Science and Humanities, Vel Tech High Tech Dr.Rangarajan Dr.Sakunthala Engineering College, Chennai 600062, India)

  • Chee Peng Lim

    (Institute for Intelligent Systems Research and Innovation, Deakin University, Geelong, VIC 3216, Australia)

  • Raja Ramachandran

    (Ramanujan Centre for Higher Mathematics, Alagappa University, Karaikudi 630004, India)

Abstract

In practical applications, stochastic effects are normally viewed as the major sources that lead to the system’s unwilling behaviours when modelling real neural systems. As such, the research on network models with stochastic effects is significant. In view of this, in this paper, we analyse the issue of robust stability for a class of uncertain complex-valued stochastic neural networks (UCVSNNs) with time-varying delays. Based on the real-imaginary separate-type activation function, the original UCVSNN model is analysed using an equivalent representation consisting of two real-valued neural networks. By constructing the proper Lyapunov–Krasovskii functional and applying Jensen’s inequality, a number of sufficient conditions can be derived by utilizing It o ^ ’s formula, the homeomorphism principle, the linear matrix inequality, and other analytic techniques. As a result, new sufficient conditions to ensure robust, globally asymptotic stability in the mean square for the considered UCVSNN models are derived. Numerical simulations are presented to illustrate the merit of the obtained results.

Suggested Citation

  • Pharunyou Chanthorn & Grienggrai Rajchakit & Jenjira Thipcha & Chanikan Emharuethai & Ramalingam Sriraman & Chee Peng Lim & Raja Ramachandran, 2020. "Robust Stability of Complex-Valued Stochastic Neural Networks with Time-Varying Delays and Parameter Uncertainties," Mathematics, MDPI, vol. 8(5), pages 1-19, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:742-:d:355233
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    References listed on IDEAS

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    Cited by:

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    5. Tranthi, Janejira & Botmart, Thongchai & Weera, Wajaree & La-inchua, Teerapong & Pinjai, Sirada, 2022. "New results on robust exponential stability of Takagi–Sugeno fuzzy for neutral differential systems with mixed time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 714-738.

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