Time delays and chaos in two competing species revisited

Akio Matsumoto and Ferenc Szidarovszky

Applied Mathematics and Computation, 2021, vol. 395, issue C

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.

Keywords: Lotka-Volterra system; Competition system; Two delays; Hopf bifurcation; Stabilliy loss and gain; Stability switching curve (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308158

DOI: 10.1016/j.amc.2020.125862

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