On the dynamics of a class of Kolmogorov systems

DOI10.1016/j.amc.2013.09.017zbMath1341.34041OpenAlexW2013155848MaRDI QIDQ5890609

Jaume Llibre, Tayeb Salhi

Publication date: 26 April 2016

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

Full work available at URL: http://ddd.uab.cat/record/150594

zbMATH Keywords

periodic orbitsintegrabilityLotka-Volterra systemsKolmogorov systems

Mathematics Subject Classification ID

Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Population dynamics (general) (92D25) Explicit solutions, first integrals of ordinary differential equations (34A05)

Related Items (14)

Nondegenerate centers and limit cycles of cubic Kolmogorov systems ⋮ Explicit expression for a first integral for some classes of two-dimensional differential systems ⋮ Bifurcation diagrams in a class of Kolmogorov systems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Analysis of a class of Kolmogorov systems ⋮ Kolmogorov differential systems with algebraic limit cycles ⋮ Unnamed Item ⋮ Multiple bifurcations of critical period for a quartic Kolmogorov model ⋮ On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems ⋮ Unnamed Item ⋮ On the dynamics of a class of rational Kolmogorov systems ⋮ A Class of Quintic Kolmogorov Systems with Explicit Non-algebraic Limit Cycle ⋮ Integrability and non-existence of periodic orbits for a class of Kolmogorov systems

Cites Work

• Unnamed Item
• Limit cycles and singular point quantities for a 3D Lotka-Volterra system
• Integrable Lotka-Volterra systems
• A 3D competitive Lotka-Volterra system with three limit cycles: a falsification of a conjecture by Hofbauer and So
• Hamiltonian structure and first integrals for the Lotka-Volterra systems
• Necessary and sufficient conditions for the existence of periodic orbits in a Lotka-Volterra system.
• Limit cycles for the competitive three dimensional Lotka-Volterra system
• Two limit cycles in three-dimensional Lotka-Volterra systems
• Limit cycles in a general Kolmogorov model
• On a Hamiltonian version of a three-dimensional Lotka-Volterra system
• Polynomial, rational and analytic first integrals for a family of 3-dimensional Lotka-Volterra systems
• Limit cycles for competitor-competitor-mutualist Lotka-Volterra systems
• Liouvillian first integrals for the planar Lotka-Volterra system
• Solving Ordinary Differential Equations I
• Global analytic first integrals for the real planar Lotka-Volterra system
• The cyclicity of period annulus of a quadratic reversible Lotka–Volterra system
• On certain new integrable second order nonlinear differential equations and their connection with two dimensional Lotka–Volterra system
• Phase portraits of cubic polynomial vector fields of Lotka–Volterra type having a rational first integral of degree 2
• LIMIT CYCLES IN 3D LOTKA–VOLTERRA SYSTEMS APPEARING AFTER PERTURBATION OF HOPF CENTER
• Lotka–Volterra systems integrable in quadratures

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