The three-dimensional generalized Lotka–Volterra systems

DOI10.1017/S0143385704000902zbMath1091.34021MaRDI QIDQ5461979

Henryk Żołądek, Marcin Bobieński

Publication date: 27 July 2005

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

zbMATH Keywords

limit cyclenormal hyperbolicityLotka-Volterra systemsPoincaré-Pontryagin-Melnikov-Arnold integral

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Periodic orbits of vector fields and flows (37C27) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Ordinary differential equations and connections with real algebraic geometry (fewnomials, desingularization, zeros of abelian integrals, etc.) (34C08)

Related Items (12)

LIMIT CYCLES IN 3D LOTKA–VOLTERRA SYSTEMS APPEARING AFTER PERTURBATION OF HOPF CENTER ⋮ Invariant torus in 3D Lotka-Volterra systems appearing after perturbation of Hopf center ⋮ Integrability and linearizability of three dimensional vector fields ⋮ Limit cycles bifurcating from a non-isolated zero-Hopf equilibrium of three-dimensional differential systems ⋮ Global dynamics of a family of 3-D Lotka–Volterra systems ⋮ INVARIANT TORUS IN 3D LOTKA–VOLTERRA SYSTEMS: THE NONDEGENERACY CONDITION ⋮ Integrability and linearizability problems of three dimensional Lotka-Volterra equations of rank-2 ⋮ Three-dimensional Lotka-Volterra systems with 3:\(-1\):2-resonance ⋮ Hopf bifurcation in 3-dimensional polynomial vector fields ⋮ Integrability and linearizability of a family of three-dimensional quadratic systems ⋮ Note on a paper of J. Llibre and G. Rodríguez concerning algebraic limit cycles ⋮ Local integrability and linearizability of three-dimensional Lotka-Volterra systems

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