Dynamics of some three-dimensional Lotka-Volterra systems

DOI10.1007/s00009-017-0927-5zbMath1376.34030OpenAlexW2609598365MaRDI QIDQ1674204

Jaume Llibre, Xiang Zhang

Publication date: 1 November 2017

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-017-0927-5

zbMATH Keywords

invariantglobal dynamicsLotka-Volterra systemphase portrait

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) Invariant manifolds for ordinary differential equations (34C45) Asymptotic properties of solutions to ordinary differential equations (34D05) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (4)

Global dynamics of 3D cooperative Lotka-Volterra system with the identical intrinsic growth rate ⋮ Unnamed Item ⋮ Global dynamics of 3D competitive Lotka-Volterra equations with the identical intrinsic growth rate ⋮ Three-dimensional Lotka-Volterra systems with 3:\(-1\):2-resonance

Cites Work

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• On the global flow of a 3-dimensional Lotka-Volterra system
• Quadratic perturbations of a quadratic reversible Lotka-Volterra system
• On the Darboux integrability of polynomial differential systems
• Polynomial, rational and analytic first integrals for a family of 3-dimensional Lotka-Volterra systems
• First integrals of Darboux type for a family of 3-dimensional Lotka-Volterra systems
• Global dynamics of the Kummer-Schwarz differential equation
• Qualitative theory of planar differential systems
• Global analytic first integrals for the real planar Lotka-Volterra system
• Bounded Polynomial Vector Fields
• Phase portraits of cubic polynomial vector fields of Lotka–Volterra type having a rational first integral of degree 2

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