IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v42y2009i1p554-559.html
   My bibliography  Save this article

Hopf bifurcation in a predator–prey system with discrete and distributed delays

Author

Listed:
  • Yang, Yu
  • Ye, Jin

Abstract

In this paper, a predator–prey system with discrete and distributed delays is considered. By regarding the delay as the bifurcation parameter and analyzing the associated characteristic equation of the original system at the positive equilibrium, it is found that Hopf bifurcations occur when the delay passes through a certain critical value. Finally, numerical simulations are given to support our theoretical results.

Suggested Citation

  • Yang, Yu & Ye, Jin, 2009. "Hopf bifurcation in a predator–prey system with discrete and distributed delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 554-559.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:1:p:554-559
    DOI: 10.1016/j.chaos.2009.01.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077909000289
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2009.01.026?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. Zheng, Baodong & Zhang, Yazhuo & Zhang, Chunrui, 2008. "Global existence of periodic solutions on a simplified BAM neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1397-1408.
    2. Li, Xiuling & Wei, Junjie, 2005. "On the zeros of a fourth degree exponential polynomial with applications to a neural network model with delays," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 519-526.
    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. 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.

    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. Yang, Yu & Ye, Jin, 2009. "Stability and bifurcation in a simplified five-neuron BAM neural network with delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2357-2363.
    2. 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.
    3. Syed Ali, M. & Balasubramaniam, P., 2009. "Global exponential stability of uncertain fuzzy BAM neural networks with time-varying delays," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2191-2199.
    4. Zhang, Chunrui & Zhang, Xianhong & Zhang, Yazhou, 2018. "Dynamic properties of feed-forward neural networks and application in contrast enhancement for image," Chaos, Solitons & Fractals, Elsevier, vol. 114(C), pages 281-290.
    5. Bera, Sovan & Khajanchi, Subhas & Roy, Tapan Kumar, 2022. "Dynamics of an HTLV-I infection model with delayed CTLs immune response," Applied Mathematics and Computation, Elsevier, vol. 430(C).
    6. Wang, Luxuan & Niu, Ben & Wei, Junjie, 2016. "Dynamical analysis for a model of asset prices with two delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 447(C), pages 297-313.
    7. Sun, Jitao & Wang, Qing-Guo & Gao, Hanqiao, 2009. "Periodic solution for nonautonomous cellular neural networks with impulses," Chaos, Solitons & Fractals, Elsevier, vol. 40(3), pages 1423-1427.
    8. Sonjoy Pan & Siddhartha P. Chakrabarty, 2020. "Hopf Bifurcation and Stability Switches Induced by Humoral Immune Delay in Hepatitis C," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(4), pages 1673-1695, December.
    9. Dipesh, & Kumar, Pankaj, 2023. "Investigating the impact of toxicity on plant growth dynamics through the zero of a fifth-degree exponential polynomial: A mathematical model using DDE," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    10. Hu Zhang & Anwar Zeb & Aying Wan & Zizhen Zhang, 2022. "Bifurcation Analysis of a Synthetic Drug Transmission Model with Two Time Delays," Mathematics, MDPI, vol. 10(9), pages 1-21, May.
    11. Çalış, Yasemin & Demirci, Ali & Özemir, Cihangir, 2022. "Hopf bifurcation of a financial dynamical system with delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 201(C), pages 343-361.
    12. Miao, Hui & Abdurahman, Xamxinur & Teng, Zhidong & Zhang, Long, 2018. "Dynamical analysis of a delayed reaction-diffusion virus infection model with logistic growth and humoral immune impairment," Chaos, Solitons & Fractals, Elsevier, vol. 110(C), pages 280-291.
    13. Kim, Kwang Su & Kim, Sangil & Jung, Il Hyo, 2018. "Hopf bifurcation analysis and optimal control of Treatment in a delayed oncolytic virus dynamics," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 1-16.
    14. Mann Manyombe, M.L. & Mbang, J. & Chendjou, G., 2021. "Stability and Hopf bifurcation of a CTL-inclusive HIV-1 infection model with both viral and cellular infections, and three delays," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    15. Sun, Dandan & Teng, Zhidong & Wang, Kai & Zhang, Tailei, 2023. "Stability and Hopf bifurcation in delayed age-structured SVIR epidemic model with vaccination and incubation," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).
    16. Xu, Changjin, 2018. "Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 69-90.
    17. Wang, Yan & Liu, Xianning, 2017. "Stability and Hopf bifurcation of a within-host chikungunya virus infection model with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 138(C), pages 31-48.
    18. Farah, El Mehdi & Amine, Saida & Allali, Karam, 2021. "Dynamics of a time-delayed two-strain epidemic model with general incidence rates," Chaos, Solitons & Fractals, Elsevier, vol. 153(P1).
    19. Zeng, Xiaocai & Xiong, Zuoliang & Wang, Changjian, 2016. "Hopf bifurcation for neutral-type neural network model with two delays," Applied Mathematics and Computation, Elsevier, vol. 282(C), pages 17-31.

    More about this item

    Statistics

    Access and download statistics

    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:chsofr:v:42:y:2009:i:1:p:554-559. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.