IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v450y2023ics0096300323001558.html
   My bibliography  Save this article

Stability and hopf bifurcation of fractional complex–valued BAM neural networks with multiple time delays

Author

Listed:
  • Hou, Hu–Shuang
  • Zhang, Hua

Abstract

In this paper dynamical behaviors of a class of high–order fractional complex–valued bidirectional associative memory neural networks with multiple time delays are investigated. Firstly, they are reduced to real–valued systems by separating the real and imaginary parts. Then, stability criteria of fractional complex–valued bidirectional associative memory neural networks without delay are obtained. Concerning the delay case, the time delay is set as a bifurcation parameter and the condition of Hopf bifurcation is given by analyzing roots of characteristic equations. Finally, two numerical examples are presented and illustrate that Hopf bifurcation does happen when time delay exceeds the critical value.

Suggested Citation

  • Hou, Hu–Shuang & Zhang, Hua, 2023. "Stability and hopf bifurcation of fractional complex–valued BAM neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 450(C).
    • Handle: RePEc:eee:apmaco:v:450:y:2023:i:c:s0096300323001558
    DOI: 10.1016/j.amc.2023.127986
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300323001558
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2023.127986?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    2. Huang, Chengdai & Meng, Yijie & Cao, Jinde & Alsaedi, Ahmed & Alsaadi, Fuad E., 2017. "New bifurcation results for fractional BAM neural network with leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 31-44.
    3. 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.
    4. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Yuan, Shuai, 2021. "Impact of leakage delay on bifurcation in fractional-order complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    Full references (including those not matched with items on IDEAS)

    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. Tu, Zhengwen & Ding, Nan & Li, Liangliang & Feng, Yuming & Zou, Limin & Zhang, Wei, 2017. "Adaptive synchronization of memristive neural networks with time-varying delays and reaction–diffusion term," Applied Mathematics and Computation, Elsevier, vol. 311(C), pages 118-128.
    2. Oliveira, José J., 2022. "Global stability criteria for nonlinear differential systems with infinite delay and applications to BAM neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 164(C).
    3. Lu, Xiaoling & Sun, Weihua, 2024. "Control and synchronization of Julia sets of discrete fractional Ising models," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    4. Xu, Changjin & Liu, Zixin & Yao, Lingyun & Aouiti, Chaouki, 2021. "Further exploration on bifurcation of fractional-order six-neuron bi-directional associative memory neural networks with multi-delays," Applied Mathematics and Computation, Elsevier, vol. 410(C).
    5. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2019. "Novel results on bifurcation for a fractional-order complex-valued neural network with leakage delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 868-883.
    6. Jiang, Xiaowei & Chen, Xiangyong & Chi, Ming & Chen, Jie, 2020. "On Hopf bifurcation and control for a delay systems," Applied Mathematics and Computation, Elsevier, vol. 370(C).
    7. Wang, Xinhe & Lu, Junwei & Wang, Zhen & Li, Yuxia, 2020. "Dynamics of discrete epidemic models on heterogeneous networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 539(C).
    8. Zhang, Lan & Yang, Xinsong & Xu, Chen & Feng, Jianwen, 2017. "Exponential synchronization of complex-valued complex networks with time-varying delays and stochastic perturbations via time-delayed impulsive control," Applied Mathematics and Computation, Elsevier, vol. 306(C), pages 22-30.
    9. Wang, Yuxiao & Cao, Yuting & Guo, Zhenyuan & Wen, Shiping, 2020. "Passivity and passification of memristive recurrent neural networks with multi-proportional delays and impulse," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    10. Qin, Xiaoli & Wang, Cong & Li, Lixiang & Peng, Haipeng & Yang, Yixian & Ye, Lu, 2018. "Finite-time modified projective synchronization of memristor-based neural network with multi-links and leakage delay," Chaos, Solitons & Fractals, Elsevier, vol. 116(C), pages 302-315.
    11. Jin-E Zhang, 2017. "Centralized and Decentralized Data-Sampling Principles for Outer-Synchronization of Fractional-Order Neural Networks," Complexity, Hindawi, vol. 2017, pages 1-11, March.
    12. Wang, Huanan & Huang, Chengdai & Liu, Heng & Cao, Jinde, 2023. "Detecting bifurcations in a fractional-order neural network with nonidentical delays via Cramer’s rule," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    13. Liao, Huaying & Zhang, Zhengqiu & Ren, Ling & Peng, Wenli, 2017. "Global asymptotic stability of periodic solutions for inertial delayed BAM neural networks via novel computing method of degree and inequality techniques," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 785-797.
    14. 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.
    15. Liang, Yuqin & Jia, Yunfeng, 2022. "Stability and Hopf bifurcation of a diffusive plankton model with time-delay and mixed nonlinear functional responses," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    16. Chen, Mengshen & Yang, Xiaofei & Shen, Hao & Yao, Fengqi, 2016. "Finite-time asynchronous H∞ control for Markov jump repeated scalar non-linear systems with input constraints," Applied Mathematics and Computation, Elsevier, vol. 275(C), pages 172-180.
    17. 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.
    18. Zhang, Hai & Chen, Xinbin & Ye, Renyu & Stamova, Ivanka & Cao, Jinde, 2023. "Adaptive quasi-synchronization analysis for Caputo delayed Cohen–Grossberg neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 212(C), pages 49-65.
    19. Syed Ali, M. & Narayanan, Govindasamy & Shekher, Vineet & Alsulami, Hamed & Saeed, Tareq, 2020. "Dynamic stability analysis of stochastic fractional-order memristor fuzzy BAM neural networks with delay and leakage terms," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    20. Călin-Adrian Popa & Eva Kaslik, 2020. "Finite-Time Mittag–Leffler Synchronization of Neutral-Type Fractional-Order Neural Networks with Leakage Delay and Time-Varying Delays," Mathematics, MDPI, vol. 8(7), pages 1-17, July.

    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:eee:apmaco:v:450:y:2023:i:c:s0096300323001558. 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: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.