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

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  • 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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    1. Dan Liu & Song Zhu & Wenting Chang, 2017. "Mean square exponential input-to-state stability of stochastic memristive complex-valued neural networks with time varying delay," International Journal of Systems Science, Taylor & Francis Journals, vol. 48(9), pages 1966-1977, July.
    2. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun & Huang, Junjian, 2018. "Synchronization of fractional-order memristor-based complex-valued neural networks with uncertain parameters and time delays," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 105-123.
    3. Cao, Yang & Samidurai, R. & Sriraman, R., 2019. "Robust passivity analysis for uncertain neural networks with leakage delay and additive time-varying delays by using general activation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 57-77.
    4. Park, Ju H., 2008. "On global stability criterion of neural networks with continuously distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(2), pages 444-449.
    5. Li, Xiaofei & Ding, Deng, 2017. "Mean square exponential stability of stochastic Hopfield neural networks with mixed delays," Statistics & Probability Letters, Elsevier, vol. 126(C), pages 88-96.
    6. Huang, He & Feng, Gang, 2007. "Delay-dependent stability for uncertain stochastic neural networks with time-varying delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 381(C), pages 93-103.
    7. Xiaohui Xu & Jibin Yang & Yanhai Xu, 2019. "Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays," Complexity, Hindawi, vol. 2019, pages 1-20, June.
    8. Wang, Zidong & Lauria, Stanislao & Fang, Jian’an & Liu, Xiaohui, 2007. "Exponential stability of uncertain stochastic neural networks with mixed time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 62-72.
    9. Wang, Zengyun & Liu, Xinzhi, 2019. "Exponential stability of impulsive complex-valued neural networks with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 143-157.
    10. Liang, Jinling & Cao, Jinde, 2006. "A based-on LMI stability criterion for delayed recurrent neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 154-160.
    11. Shi, Yanchao & Cao, Jinde & Chen, Guanrong, 2017. "Exponential stability of complex-valued memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 222-234.
    12. Samidurai, R. & Sriraman, R., 2019. "Robust dissipativity analysis for uncertain neural networks with additive time-varying delays and general activation functions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 155(C), pages 201-216.
    13. Cao, Yang & Sriraman, R. & Shyamsundarraj, N. & Samidurai, R., 2020. "Robust stability of uncertain stochastic complex-valued neural networks with additive time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 207-220.
    14. Chen, Xiaofeng & Zhao, Zhenjiang & Song, Qiankun & Hu, Jin, 2017. "Multistability of complex-valued neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 18-35.
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    Cited by:

    1. Rajchakit, G. & Sriraman, R. & Lim, C.P. & Unyong, B., 2022. "Existence, uniqueness and global stability of Clifford-valued neutral-type neural networks with time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 508-527.
    2. Jianying Xiao & Yongtao Li, 2022. "Novel Synchronization Conditions for the Unified System of Multi-Dimension-Valued Neural Networks," Mathematics, MDPI, vol. 10(17), pages 1-24, August.
    3. Fan, Gaofeng & Ma, Yuechao, 2023. "Fault-tolerant fixed/preassigned-time synchronization control of uncertain singularly perturbed complex networks with time-varying delay and stochastic disturbances," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    4. 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.
    5. Pengfei Guo & Yunong Zhang, 2022. "Tracking Control for Triple-Integrator and Quintuple-Integrator Systems with Single Input Using Zhang Neural Network with Time Delay Caused by Backward Finite-Divided Difference Formulas for Multiple-," Mathematics, MDPI, vol. 10(9), pages 1-27, April.
    6. K., Pooja Lakshmi & Senthilkumar, T., 2024. "Synchronization results for uncertain complex-valued neural networks under delay-dependent flexible impulsive control," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).

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