Periodic orbits bifurcating from a Hopf equilibrium of 2-dimensional polynomial Kolmogorov systems of arbitrary degree

Djamila Djedid, Jaume Llibre and Amar Makhlouf

Chaos, Solitons & Fractals, 2021, vol. 142, issue C

Abstract: A Hopf equilibrium of a differential system in R2 is an equilibrium point whose linear part has eigenvalues ±ωi with ω≠0, where i=−1. We provide necessary and sufficient conditions for the existence of a limit cycle bifurcating from a Hopf equilibrium of 2–dimensional polynomial Kolmogorov systems of arbitrary degree. We provide an estimation of the bifurcating small limit cycle and also characterize the stability of this limit cycle.

Keywords: Lotka-Volterra system; Periodic orbit; Averaging theory; Zero Hopf bifurcation; Zero–Hopf equilibria (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:142:y:2021:i:c:s096007792030881x

DOI: 10.1016/j.chaos.2020.110489

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