Center-focus problem and limit cycles bifurcations for a class of cubic Kolmogorov model

DOI10.1007/s11071-012-0703-9zbMath1269.92065OpenAlexW1972744150MaRDI QIDQ354997

Wen-tao Huang, Chao-xiong Du

Publication date: 22 July 2013

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-012-0703-9

zbMATH Keywords

stabilitycenter problemPoincaré succession functionpositive equilibrium points

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Ecology (92D40)

Related Items (11)

Nondegenerate centers and limit cycles of cubic Kolmogorov systems ⋮ Integrability and non-linearizability of weak saddles in a cubic Kolmogorov model ⋮ Small amplitude limit cycles and local bifurcation of critical periods for a quartic Kolmogorov system ⋮ Bifurcation of limit cycles and isochronous centers on center manifolds for a class of cubic Kolmogorov systems in \(\mathbb{R}^3\) ⋮ LIMIT CYCLE BIFURCATION FOR A NILPOTENT SYSTEM IN <i>Z</i>₃-EQUIVARIANT VECTOR FIELD ⋮ Limit cycles in a cubic Kolmogorov system with harvest and two positive equilibrium points ⋮ Multiple bifurcations of critical period for a quartic Kolmogorov model ⋮ Double bifurcation for a cubic Kolmogorov model ⋮ Center problem and the bifurcation of limit cycles for a cubic polynomial system ⋮ Behavior of limit cycle bifurcations for a class of quartic Kolmogorov models in a symmetrical vector field ⋮ Limit Cycles in a Class of Quartic Kolmogorov Model with Three Positive Equilibrium Points

Cites Work

• The limit cycles of a general Kolmogorov system
• The bifurcation of limit cycles in \(Z_n\)-equivariant vector fields
• Limit cycles in a general Kolmogorov model
• A cubic Kolmogorov system with six limit cycles
• Limit cycles of a cubic Kolmogorov system
• Unnamed Item

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