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Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability

Author

Listed:
  • Usa Humphries

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru 10140, Thailand)

  • Grienggrai Rajchakit

    (Department of Mathematics, Faculty of Science, Maejo University, Chiang Mai 50290, Thailand)

  • Pramet Kaewmesri

    (Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thung Khru 10140, Thailand)

  • Pharunyou Chanthorn

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

  • Ramalingam Sriraman

    (Department of Science and Humanities, Vel Tech High Tech Dr. Rangarajan Dr. Sakunthala Engineering College, Avadi, Tamil Nadu 600 062, India)

  • Rajendran Samidurai

    (Department of Mathematics, Thiruvalluvar University, Vellore, Tamil Nadu 632115, India)

  • Chee Peng Lim

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

Abstract

In this paper, we study the mean-square exponential input-to-state stability (exp-ISS) problem for a new class of neural network (NN) models, i.e., continuous-time stochastic memristive quaternion-valued neural networks (SMQVNNs) with time delays. Firstly, in order to overcome the difficulties posed by non-commutative quaternion multiplication, we decompose the original SMQVNNs into four real-valued models. Secondly, by constructing suitable Lyapunov functional and applying It o ^ ’s formula, Dynkin’s formula as well as inequity techniques, we prove that the considered system model is mean-square exp-ISS. In comparison with the conventional research on stability, we derive a new mean-square exp-ISS criterion for SMQVNNs. The results obtained in this paper are the general case of previously known results in complex and real fields. Finally, a numerical example has been provided to show the effectiveness of the obtained theoretical results.

Suggested Citation

  • Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Stochastic Memristive Quaternion-Valued Neural Networks with Time Delays: An Analysis on Mean Square Exponential Input-to-State Stability," Mathematics, MDPI, vol. 8(5), pages 1-26, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:815-:d:359619
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    References listed on IDEAS

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    Cited by:

    1. Zeng, Runtian & Song, Qiankun, 2024. "Mean-square exponential input-to-state stability for stochastic neutral-type quaternion-valued neural networks via Itô’s formula of quaternion version," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    2. 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.
    3. Iswarya, M. & Raja, R. & Cao, J. & Niezabitowski, M. & Alzabut, J. & Maharajan, C., 2022. "New results on exponential input-to-state stability analysis of memristor based complex-valued inertial neural networks with proportional and distributed delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 440-461.
    4. 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.

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