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Time delays and chaos in two competing species revisited

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  • 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
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    References listed on IDEAS

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    1. Akio Matsumoto & Ferenc Szidarovszky, 2018. "Dynamic Oligopolies with Time Delays," Springer Books, Springer, number 978-981-13-1786-6, January.
    2. 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.
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