IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v474y2024ics0096300324001565.html
   My bibliography  Save this article

Stability analysis and Hopf bifurcation for two-species reaction-diffusion-advection competition systems with two time delays

Author

Listed:
  • Alfifi, H.Y.

Abstract

This paper examines a class of two-species reaction-diffusion-advection competition models with two time delays. A system of DDE equations was derived, both theoretically and numerically, using the Galerkin technique method. A condition is defined that helps to find the existence of Hopf bifurcation points. Full diagrams of the Hopf bifurcation points and areas of stability are investigated in detail. Furthermore, we discuss three different sources of delay on bifurcation maps, and what impacts of all these cases of delays on others free rates on the regions of the Hopf bifurcation in this model. We find two different stability regions when the delay time is positive (τ>0), while the no-delay case (τ=0) has only one stable region. Moreover, the effect of delays and diffusion rates on all free others parameters in this model have been considered, which can significantly impact upon the stability regions in both population concentrations. It is also found that, as diffusion increases, the time delay increases. However, as the delay maturation is increased, the Hopf points for both proliferation of the population and advection rates are decreased and it causes raises to the region of instability. In addition, bifurcation diagrams are drawn to display chosen instances of the periodic oscillation and two dimensional phase portraits for both concentrations have been plotted to corroborate all analytical outputs that investigated in the theoretical part.

Suggested Citation

  • Alfifi, H.Y., 2024. "Stability analysis and Hopf bifurcation for two-species reaction-diffusion-advection competition systems with two time delays," Applied Mathematics and Computation, Elsevier, vol. 474(C).
    • Handle: RePEc:eee:apmaco:v:474:y:2024:i:c:s0096300324001565
    DOI: 10.1016/j.amc.2024.128684
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300324001565
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2024.128684?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. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    2. Alfifi, H.Y., 2023. "Effects of diffusion and delayed immune response on dynamic behavior in a viral model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    3. Canabarro, A.A. & Gléria, I.M. & Lyra, M.L., 2004. "Periodic solutions and chaos in a non-linear model for the delayed cellular immune response," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 342(1), pages 234-241.
    4. H. Y. Alfifi & Baogui Xin, 2021. "Semi-Analytical Solutions for the Diffusive Kaldor–Kalecki Business Cycle Model with a Time Delay for Gross Product and Capital Stock," Complexity, Hindawi, vol. 2021, pages 1-10, May.
    5. Alfifi, H.Y., 2021. "Stability and Hopf bifurcation analysis for the diffusive delay logistic population model with spatially heterogeneous environment," Applied Mathematics and Computation, Elsevier, vol. 408(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. Alfifi, H.Y., 2023. "Effects of diffusion and delayed immune response on dynamic behavior in a viral model," Applied Mathematics and Computation, Elsevier, vol. 441(C).
    2. Alfifi, H.Y., 2022. "Stability analysis for Schnakenberg reaction-diffusion model with gene expression time delay," Chaos, Solitons & Fractals, Elsevier, vol. 155(C).
    3. Bai, Zhenguo & Zhou, Yicang, 2012. "Dynamics of a viral infection model with delayed CTL response and immune circadian rhythm," Chaos, Solitons & Fractals, Elsevier, vol. 45(9), pages 1133-1139.
    4. Li, Yanqiu & Zhou, Yibo, 2023. "Turing–Hopf bifurcation in a general Selkov–Schnakenberg reaction–diffusion system," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    5. Zuo, X.Q. & Fan, Y.S., 2006. "A chaos search immune algorithm with its application to neuro-fuzzy controller design," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 94-109.
    6. John C. Eckalbar & Pete Tsournos & Walter L. Eckalbar, 2015. "Dynamics In An Sir Model When Vaccination Demand Follows Prior Levels Of Disease Prevalence," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 18(07n08), pages 1-27, November.
    7. Haibin Wang & Rui Xu, 2013. "Stability and Hopf Bifurcation in an HIV-1 Infection Model with Latently Infected Cells and Delayed Immune Response," Discrete Dynamics in Nature and Society, Hindawi, vol. 2013, pages 1-12, December.

    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:474:y:2024:i:c:s0096300324001565. 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.