IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v395y2021ics0096300320308158.html
   My bibliography  Save this article

Time delays and chaos in two competing species revisited

Author

Listed:
  • Matsumoto, Akio
  • Szidarovszky, Ferenc

Abstract

This paper reexamines the Lotka-Volterra competition model with two delays. The steady state is shown to be locally asymptotically stable without delay. If the two delays are identical, then the model becomes a one-delay system. The critical value of the delay is determined when stability might be lost. If the delays are different, then the stability switching curves are analytically defined and numerically verified. It is demonstrated that the unstable two-delay system may exhibit periodic behavior, multistability, quasi period-doubling cascade and even complicated dynamics depending on model parameters.

Suggested Citation

  • Matsumoto, Akio & Szidarovszky, Ferenc, 2021. "Time delays and chaos in two competing species revisited," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308158
    DOI: 10.1016/j.amc.2020.125862
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300320308158
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2020.125862?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. Matsumoto, Akio & Szidarovszky, Ferenc, 2020. "Stability switching curves in a Lotka–Volterra competition system with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 422-438.
    2. Akio Matsumoto & Ferenc Szidarovszky, 2018. "Dynamic Oligopolies with Time Delays," Springer Books, Springer, number 978-981-13-1786-6, July.
    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. S. Kabaivanov & V. Zhelinski & B. Zlatanov, 2021. "Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions," Papers 2110.01496, arXiv.org.
    2. Akio Matsumoto & Ferenc Szidarovszky & Maryam Hamidi, 2023. "On a Special Two-Person Dynamic Game," Games, MDPI, vol. 14(6), pages 1-22, October.
    3. Akio Matsumoto & Ferenc Szidarovszky & Keiko Nakayama, 2020. "Delay Cournot Duopoly Game with Gradient Adjustment: Berezowski Transition from a Discrete Model to a Continuous Model," Mathematics, MDPI, vol. 9(1), pages 1-19, December.
    4. Matsumoto, Akio & Szidarovszky, Ferenc, 2022. "The chaotic monopolist revisited with bounded rationality and delay dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    5. Akio Matsumoto & Ferenc Szidarovszky, 2020. "Delay Stability of n -Firm Cournot Oligopolies," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    6. Laura Ajeti & Atanas Ilchev & Boyan Zlatanov, 2022. "On Coupled Best Proximity Points in Reflexive Banach Spaces," Mathematics, MDPI, vol. 10(8), pages 1-19, April.
    7. Yulia Dzhabarova & Stanimir Kabaivanov & Margarita Ruseva & Boyan Zlatanov, 2020. "Existence, Uniqueness and Stability of Market Equilibrium in Oligopoly Markets," Administrative Sciences, MDPI, vol. 10(3), pages 1-32, September.
    8. Pati, N.C. & Ghosh, Bapan, 2022. "Delayed carrying capacity induced subcritical and supercritical Hopf bifurcations in a predator–prey system," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 195(C), pages 171-196.
    9. Matsumoto, Akio & Szidarovszky, Ferenc, 2023. "Delay Solow Model with a Normalized CES Production Function," Journal of Economic Behavior & Organization, Elsevier, vol. 213(C), pages 305-323.
    10. Ferenc Szidarovszky & Akio Matsumoto, 2024. "Dynamic Cooperative Oligopolies," Mathematics, MDPI, vol. 12(6), pages 1-12, March.
    11. Akio Matsumoto & Ferenc Szidarovszky, 2022. "Stability of dynamic asymmetric contests with endogenous prizes," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 17(1), pages 29-40, January.
    12. Akio Matsumoto & Ferenc Szidarovszky, 2021. "Delay two-sector economic growth model with a Cobb–Douglas production function," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 341-358, June.
    13. Matsumoto, Akio & Szidarovszky, Ferenc, 2020. "Stability switching curves in a Lotka–Volterra competition system with two delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 178(C), pages 422-438.
    14. Anton Badev & Stanimir Kabaivanov & Petar Kopanov & Vasil Zhelinski & Boyan Zlatanov, 2024. "Long-Run Equilibrium in the Market of Mobile Services in the USA," Mathematics, MDPI, vol. 12(5), pages 1-21, February.
    15. Matsumoto, Akio & Szidarovszky, Ferenc, 2020. "Delay growth model augmented with physical and human capitals," Chaos, Solitons & Fractals, Elsevier, vol. 130(C).
    16. Culda, Loredana Camelia & Kaslik, Eva & Neamţu, Mihaela, 2022. "Stability and bifurcations in a general Cournot duopoly model with distributed time delays," Chaos, Solitons & Fractals, Elsevier, vol. 162(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:395:y:2021:i:c:s0096300320308158. 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.