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

DOI10.1016/j.chaos.2020.110489zbMath1496.34064OpenAlexW3108643544MaRDI QIDQ2128285

Djamila Djedid, Amar Makhlouf, Jaume Llibre

Publication date: 21 April 2022

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2020.110489

zbMATH Keywords

periodic orbitLotka-Volterra systemaveraging theoryzero Hopf bifurcationzero-Hopf equilibria

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Bifurcation theory for ordinary differential equations (34C23) Averaging method for ordinary differential equations (34C29) Bifurcations of singular points in dynamical systems (37G10)

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On the Local Stability of a Certain Class of Polynomial Differential System

Cites Work

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• Nondegenerate centers and limit cycles of cubic Kolmogorov systems
• Analytical integrability problem for perturbations of cubic Kolmogorov systems
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• A survey of quadratic systems
• Hopf bifurcation at infinity and dissipative vector fields of the plane
• Three-Dimensional Hopf Bifurcation for a Class of Cubic Kolmogorov Model
• The dynamical behaviour of type-K competitive Kolmogorov systems and its application to three-dimensional type-K competitive Lotka Volterra systems
• Averaging methods in nonlinear dynamical systems

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