IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v8y2020i5p815-d359619.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/8/5/815/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/8/5/815/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    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. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    3. 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.
    4. Qi, Xingnan & Bao, Haibo & Cao, Jinde, 2019. "Exponential input-to-state stability of quaternion-valued neural networks with time delay," Applied Mathematics and Computation, Elsevier, vol. 358(C), pages 382-393.
    5. James M. Tour & Tao He, 2008. "The fourth element," Nature, Nature, vol. 453(7191), pages 42-43, May.
    6. Goh, S.L. & Chen, M. & Popović, D.H. & Aihara, K. & Obradovic, D. & Mandic, D.P., 2006. "Complex-valued forecasting of wind profile," Renewable Energy, Elsevier, vol. 31(11), pages 1733-1750.
    7. Tu, Zhengwen & Zhao, Yongxiang & Ding, Nan & Feng, Yuming & Zhang, Wei, 2019. "Stability analysis of quaternion-valued neural networks with both discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 342-353.
    8. Xiaofei Li & Deng Ding & Di Sang, 2018. "Exponential stability of stochastic cellular neural networks with mixed delays," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(19), pages 4881-4894, October.
    9. Park, Ju H. & Kwon, O.M., 2009. "Global stability for neural networks of neutral-type with interval time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1174-1181.
    10. Dmitri B. Strukov & Gregory S. Snider & Duncan R. Stewart & R. Stanley Williams, 2008. "The missing memristor found," Nature, Nature, vol. 453(7191), pages 80-83, May.
    11. Guo, Runan & Zhang, Ziye & Liu, Xiaoping & Lin, Chong, 2017. "Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 100-117.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Grienggrai Rajchakit & Pharunyou Chanthorn & Pramet Kaewmesri & Ramalingam Sriraman & Chee Peng Lim, 2020. "Global Mittag–Leffler Stability and Stabilization Analysis of Fractional-Order Quaternion-Valued Memristive Neural Networks," Mathematics, MDPI, vol. 8(3), pages 1-29, March.
    2. Usa Humphries & Grienggrai Rajchakit & Pramet Kaewmesri & Pharunyou Chanthorn & Ramalingam Sriraman & Rajendran Samidurai & Chee Peng Lim, 2020. "Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks," Mathematics, MDPI, vol. 8(5), pages 1-27, May.
    3. Chang, Wenting & Zhu, Song & Li, Jinyu & Sun, Kaili, 2018. "Global Mittag–Leffler stabilization of fractional-order complex-valued memristive neural networks," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 346-362.
    4. 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.
    5. Sriraman, R. & Cao, Yang & Samidurai, R., 2020. "Global asymptotic stability of stochastic complex-valued neural networks with probabilistic time-varying delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 171(C), pages 103-118.
    6. Mathiyalagan, K. & Park, Ju H. & Sakthivel, R., 2015. "Synchronization for delayed memristive BAM neural networks using impulsive control with random nonlinearities," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 967-979.
    7. Min, Fuhong & Zhang, Wen & Ji, Ziyi & Zhang, Lei, 2021. "Switching dynamics of a non-autonomous FitzHugh-Nagumo circuit with piecewise-linear flux-controlled memristor," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    8. Luo, Mengzhuo & Cheng, Jun & Liu, Xinzhi & Zhong, Shouming, 2019. "An extended synchronization analysis for memristor-based coupled neural networks via aperiodically intermittent control," Applied Mathematics and Computation, Elsevier, vol. 344, pages 163-182.
    9. Liu, Shuxin & Yu, Yongguang & Zhang, Shuo & Zhang, Yuting, 2018. "Robust stability of fractional-order memristor-based Hopfield neural networks with parameter disturbances," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 845-854.
    10. Sakthivel, R. & Anbuvithya, R. & Mathiyalagan, K. & Ma, Yong-Ki & Prakash, P., 2016. "Reliable anti-synchronization conditions for BAM memristive neural networks with different memductance functions," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 213-228.
    11. Pan, Jie & Pan, Zhaoya, 2021. "Novel robust stability criteria for uncertain parameter quaternionic neural networks with mixed delays: Whole quaternionic method," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    12. Bao, Haibo & Park, Ju H. & Cao, Jinde, 2015. "Matrix measure strategies for exponential synchronization and anti-synchronization of memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 543-556.
    13. Guo, Runan & Zhang, Ziye & Liu, Xiaoping & Lin, Chong, 2017. "Existence, uniqueness, and exponential stability analysis for complex-valued memristor-based BAM neural networks with time delays," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 100-117.
    14. Tu, Zhengwen & Yang, Xinsong & Wang, Liangwei & Ding, Nan, 2019. "Stability and stabilization of quaternion-valued neural networks with uncertain time-delayed impulses: Direct quaternion method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    15. Yang, Shuai & Hu, Cheng & Yu, Juan & Jiang, Haijun, 2021. "Projective synchronization in finite-time for fully quaternion-valued memristive networks with fractional-order," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    16. Jie Pan & Lianglin Xiong, 2021. "Novel Criteria of Stability for Delayed Memristive Quaternionic Neural Networks: Directly Quaternionic Method," Mathematics, MDPI, vol. 9(11), pages 1-14, June.
    17. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin & Wu, Tao & Zhang, Haiyang, 2021. "Stochastic stabilization of Markov jump quaternion-valued neural network using sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 400(C).
    18. Shu, Jinlong & Wu, Baowei & Xiong, Lianglin, 2022. "Stochastic stability criteria and event-triggered control of delayed Markovian jump quaternion-valued neural networks," Applied Mathematics and Computation, Elsevier, vol. 420(C).
    19. 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.
    20. Zhang, Lingzhong & Yang, Yongqing & Xu, Xianyun, 2018. "Synchronization analysis for fractional order memristive Cohen–Grossberg neural networks with state feedback and impulsive control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 644-660.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:815-:d:359619. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.