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Stability switching curves in a Lotka–Volterra competition system with two delays

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  • Matsumoto, Akio
  • Szidarovszky, Ferenc

Abstract

This study is devoted to consider the dynamic properties of a Lotka–Volterra competition model with two discrete delays. First, it reviews stability conditions of the no-delay model as a benchmark. Second, it examines the delay model and analytically establishes the stability switching curve on which stability is switched to instability and vice versa. Finally, numerical simulations are performed to confirm the theoretical results such as Hopf bifurcations and, further, demonstrate a wide variety of dynamics ranging from simple limit cycle to the existence of multi-stability and the birth of chaotic dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:178:y:2020:i:c:p:422-438
    DOI: 10.1016/j.matcom.2020.06.017
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    1. 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.
    2. Akio Matsumoto & Ferenc Szidarovszky, 2018. "Dynamic Oligopolies with Time Delays," Springer Books, Springer, number 978-981-13-1786-6, December.
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    Cited by:

    1. 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.
    2. Matsumoto, Akio & Szidarovszky, Ferenc, 2021. "Time delays and chaos in two competing species revisited," Applied Mathematics and Computation, Elsevier, vol. 395(C).

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