IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v330y2018icp152-169.html
   My bibliography  Save this article

Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays

Author

Listed:
  • Li, Li
  • Wang, Zhen
  • Li, Yuxia
  • Shen, Hao
  • Lu, Junwei

Abstract

In this paper, a class of complex-valued neural network model with discrete and distributed delays is proposed. Regarding the discrete time delay as the bifurcating parameter, the problem of Hopf bifurcation in the newly-proposed complex-valued neural network model is investigated under the assumption that the activation function can be separated into its real and imaginary parts. Based on the normal form theory and center manifold theorem, some sufficient conditions which determine the direction of the Hopf bifurcation and the stability of the bifurcating periodic solutions are established. Finally, a numerical example is given to illustrate the validity of the theoretical results.

Suggested Citation

  • Li, Li & Wang, Zhen & Li, Yuxia & Shen, Hao & Lu, Junwei, 2018. "Hopf bifurcation analysis of a complex-valued neural network model with discrete and distributed delays," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 152-169.
    • Handle: RePEc:eee:apmaco:v:330:y:2018:i:c:p:152-169
    DOI: 10.1016/j.amc.2018.02.029
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300318301310
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2018.02.029?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. Liang, Kun & Dai, Mingcheng & Shen, Hao & Wang, Jing & Wang, Zhen & Chen, Bo, 2018. "L2−L∞ synchronization for singularly perturbed complex networks with semi-Markov jump topology," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 450-462.
    2. 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.
    3. Sabri Arik, 2016. "Dynamical analysis of uncertain neural networks with multiple time delays," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(3), pages 730-739, February.
    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. Harshavarthini, S. & Sakthivel, R. & Ma, Yong-Ki & Muslim, M., 2020. "Finite-time resilient fault-tolerant investment policy scheme for chaotic nonlinear finance system," Chaos, Solitons & Fractals, Elsevier, vol. 132(C).
    2. Kai, Yue & Chen, Shuangqing & Zheng, Bailin & Zhang, Kai & Yang, Nan & Xu, Wenlong, 2020. "Qualitative and quantitative analysis of nonlinear dynamics by the complete discrimination system for polynomial method," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    3. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Zhang, Minsong & Ding, Ling & Cao, Jinde & Alsaedi, Ahmed, 2020. "Dynamic optimal control of enhancing feedback treatment for a delayed fractional order predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 554(C).
    4. Hao, Zhang & Xing-yuan, Wang & Peng-fei, Yan & Yu-jie, Sun, 2020. "Combination synchronization and stability analysis of time-varying complex-valued neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 131(C).
    5. Ziye Zhang & Xiaoping Liu & Chong Lin & Bing Chen, 2018. "Finite-Time Synchronization for Complex-Valued Recurrent Neural Networks with Time Delays," Complexity, Hindawi, vol. 2018, pages 1-14, December.
    6. Zhou, Weigang & Huang, Chengdai & Xiao, Min & Cao, Jinde, 2019. "Hybrid tactics for bifurcation control in a fractional-order delayed predator–prey model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 183-191.
    7. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    8. Huang, Chengdai & Li, Huan & Cao, Jinde, 2019. "A novel strategy of bifurcation control for a delayed fractional predator–prey model," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 808-838.
    9. Hu, Xiaohui & Xia, Jianwei & Wei, Yunliang & Meng, Bo & Shen, Hao, 2019. "Passivity-based state synchronization for semi-Markov jump coupled chaotic neural networks with randomly occurring time delays," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 32-41.
    10. Liu, Fuxiang & Yang, Ruizhi & Tang, Leiyu, 2019. "Hopf bifurcation in a diffusive predator-prey model with competitive interference," Chaos, Solitons & Fractals, Elsevier, vol. 120(C), pages 250-258.
    11. Tong, Liyun & Liu, Yang & Lou, Jungang & Lu, Jianquan & Alsaadi, Fuad E., 2018. "Static output feedback set stabilization for context-sensitive probabilistic Boolean control networks," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 263-275.
    12. Yuan, Jun & Zhao, Lingzhi & Huang, Chengdai & Xiao, Min, 2021. "Stability and bifurcation analysis of a fractional predator–prey model involving two nonidentical delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 181(C), pages 562-580.
    13. Tang, Xiaosong, 2022. "Periodic solutions and spatial patterns induced by mixed delays in a diffusive spruce budworm model with Holling II predation function," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 192(C), pages 420-429.
    14. Huang, Zhengguo & Xia, Jianwei & Wang, Jing & Wei, Yunliang & Wang, Zhen & Wang, Jian, 2019. "Mixed H∞/l2−l∞ state estimation for switched genetic regulatory networks subject to packet dropouts: A persistent dwell-time switching mechanism," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 198-212.
    15. Huang, Yao & Bao, Haibo, 2020. "Master-slave synchronization of complex-valued delayed chaotic Lur’e systems with sampled-data control," Applied Mathematics and Computation, Elsevier, vol. 379(C).
    16. Wang, Yanqian & Chen, Fu & Zhuang, Guangming & Yang, Guang, 2020. "Dynamic event-based mixed H∞ and dissipative asynchronous control for Markov jump singularly perturbed systems," Applied Mathematics and Computation, Elsevier, vol. 386(C).
    17. Huang, Chengdai & Liu, Heng & Chen, Xiaoping & Cao, Jinde & Alsaedi, Ahmed, 2020. "Extended feedback and simulation strategies for a delayed fractional-order control system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    18. 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).
    19. Yang, Te & Chen, Guoliang & Xia, Jianwei & Wang, Zhen & Sun, Qun, 2019. "Robust H∞ filtering for polytopic uncertain stochastic systems under quantized sampled outputs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 688-701.
    20. Xu, Changjin & Liao, Maoxin & Li, Peiluan & Guo, Ying & Xiao, Qimei & Yuan, Shuai, 2019. "Influence of multiple time delays on bifurcation of fractional-order neural networks," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 565-582.
    21. Chen, Yonggang & Wang, Zidong & Liu, Yurong & Alsaadi, Fuad E., 2018. "Stochastic stability for distributed delay neural networks via augmented Lyapunov–Krasovskii functionals," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 869-881.
    22. Changjin Xu & Peiluan Li & Maoxin Liao & Zixin Liu & Qimei Xiao & Shuai Yuan, 2019. "Control Scheme for a Fractional-Order Chaotic Genesio-Tesi Model," Complexity, Hindawi, vol. 2019, pages 1-15, September.

    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. Long, Shaohua & Wu, Yunlong & Zhong, Shouming & Zhang, Dian, 2018. "Stability analysis for a class of neutral type singular systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 339(C), pages 113-131.
    2. Ziye Zhang & Xiaoping Liu & Chong Lin & Bing Chen, 2018. "Finite-Time Synchronization for Complex-Valued Recurrent Neural Networks with Time Delays," Complexity, Hindawi, vol. 2018, pages 1-14, December.
    3. Li, Yankai & Chen, Mou & Li, Tao & Shi, Peng, 2020. "Anti-disturbance reference mode resilient dynamic output feedback control for turbofan systems," Applied Mathematics and Computation, Elsevier, vol. 378(C).
    4. Wang, Chen & Zhang, Hai & Ye, Renyu & Zhang, Weiwei & Zhang, Hongmei, 2023. "Finite time passivity analysis for Caputo fractional BAM reaction–diffusion delayed neural networks," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 424-443.
    5. 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).
    6. Wang, Jing & Liang, Kun & Huang, Xia & Wang, Zhen & Shen, Hao, 2018. "Dissipative fault-tolerant control for nonlinear singular perturbed systems with Markov jumping parameters based on slow state feedback," Applied Mathematics and Computation, Elsevier, vol. 328(C), pages 247-262.
    7. Shan, Yaonan & She, Kun & Zhong, Shouming & Zhong, Qishui & Shi, Kaibo & Zhao, Can, 2018. "Exponential stability and extended dissipativity criteria for generalized discrete-time neural networks with additive time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 333(C), pages 145-168.
    8. Zhen Yang & Zhengqiu Zhang, 2022. "Finite-Time Synchronization Analysis for BAM Neural Networks with Time-Varying Delays by Applying the Maximum-Value Approach with New Inequalities," Mathematics, MDPI, vol. 10(5), pages 1-16, March.
    9. Jiao, Shiyu & Shen, Hao & Wei, Yunliang & Huang, Xia & Wang, Zhen, 2018. "Further results on dissipativity and stability analysis of Markov jump generalized neural networks with time-varying interval delays," Applied Mathematics and Computation, Elsevier, vol. 336(C), pages 338-350.
    10. Zhuang, Guangming & Xu, Shengyuan & Xia, Jianwei & Ma, Qian & Zhang, Zhengqiang, 2019. "Non-fragile delay feedback control for neutral stochastic Markovian jump systems with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 355(C), pages 21-32.
    11. Jinlong Shu & Lianglin Xiong & Tao Wu & Zixin Liu, 2019. "Stability Analysis of Quaternion-Valued Neutral-Type Neural Networks with Time-Varying Delay," Mathematics, MDPI, vol. 7(1), pages 1-23, January.
    12. Tan, Lihua & Li, Chuandong & Huang, Junjian & Huang, Tingwen, 2021. "Output feedback leader-following consensus for nonlinear stochastic multiagent systems: The event-triggered method," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    13. Yang, Te & Chen, Guoliang & Xia, Jianwei & Wang, Zhen & Sun, Qun, 2019. "Robust H∞ filtering for polytopic uncertain stochastic systems under quantized sampled outputs," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 688-701.
    14. 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.
    15. Subramanian, K. & Muthukumar, P. & Lakshmanan, S., 2018. "State feedback synchronization control of impulsive neural networks with mixed delays and linear fractional uncertainties," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 267-281.
    16. Fan, Ming-Can & Wu, Yue, 2018. "Global leader-following consensus of nonlinear multi-agent systems with unknown control directions and unknown external disturbances," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 274-286.
    17. Zhang, Dian & Cheng, Jun & Ki Ahn, Choon & Ni, Hongjie, 2019. "A flexible terminal approach to stochastic stability and stabilization of continuous-time semi-Markovian jump systems with time-varying delay," Applied Mathematics and Computation, Elsevier, vol. 342(C), pages 191-205.
    18. 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.
    19. 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.
    20. Yu, Peng & Ma, Yuechao, 2020. "Observer-based asynchronous control for Markov jump systems," Applied Mathematics and Computation, Elsevier, vol. 377(C).

    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:330:y:2018:i:c:p:152-169. 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.