Limit cycles and singular point quantities for a 3D Lotka-Volterra system

DOI10.1016/j.amc.2011.03.113zbMath1220.34051OpenAlexW2074953783MaRDI QIDQ546068

Bai-Lian Li, Wen-tao Huang, Qin-long Wang

Publication date: 24 June 2011

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2011.03.113

zbMATH Keywords

Hopf bifurcationcenter manifold3D Lotka-Volterra systemsingular point quantities

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) Population dynamics (general) (92D25) Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations (34C07) Invariant manifolds for ordinary differential equations (34C45)

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Uses Software

• Mathematica

Cites Work

• Three limit cycles for a three-dimensional Lotka-Volterra competitive system with a heteroclinic cycle
• Hopf bifurcation for a class of three-dimensional nonlinear dynamic systems
• A 3D competitive Lotka-Volterra system with three limit cycles: a falsification of a conjecture by Hofbauer and So
• Four limit cycles for a three-dimensional competitive Lotka-Volterra system with a heteroclinic cycle
• Multiple limit cycles for three dimensional Lotka-Volterra equations
• Limit cycles for the competitive three dimensional Lotka-Volterra system
• Two limit cycles in three-dimensional Lotka-Volterra systems
• Hopf bifurcations in competitive three-dimensional Lotka–Volterra systems

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