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

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  • Djedid, Djamila
  • Llibre, Jaume
  • Makhlouf, Amar

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.

Suggested Citation

  • Djedid, Djamila & Llibre, Jaume & Makhlouf, Amar, 2021. "Periodic orbits bifurcating from a Hopf equilibrium of 2-dimensional polynomial Kolmogorov systems of arbitrary degree," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    • Handle: RePEc:eee:chsofr:v:142:y:2021:i:c:s096007792030881x
    DOI: 10.1016/j.chaos.2020.110489
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    References listed on IDEAS

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    1. Algaba, Antonio & García, Cristóbal & Reyes, Manuel, 2018. "Analytical integrability problem for perturbations of cubic Kolmogorov systems," Chaos, Solitons & Fractals, Elsevier, vol. 113(C), pages 1-10.
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