Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in \(\mathbb{R}_+^4\)

DOI10.1016/j.jde.2016.10.042zbMath1354.37061OpenAlexW2551310300MaRDI QIDQ729945

Jaume Llibre, Dongmei Xiao

Publication date: 22 December 2016

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2016.10.042

zbMATH Keywords

Hamiltonian systemhypersurfacesglobal dynamicstopological classificationLiouvillian integrability

Mathematics Subject Classification ID

Related Items (3)

Invariant circles and phase portraits of cubic vector fields on the sphere ⋮ Analysis of a class of Kolmogorov systems ⋮ On the configurations of centers of planar Hamiltonian Kolmogorov cubic polynomial differential systems

Cites Work

• The global phase space for the 2- and 3-dimensional Kepler problems
• Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems
• On the differential equations of species in competition
• The period function of a Hamiltonian quadratic system
• Limit cycles for the competitive three dimensional Lotka-Volterra system
• Darboux theory of integrability in \(\mathbb C^n\) taking into account the multiplicity
• Qualitative theory of planar differential systems
• Stability and convergence in strongly monotone dynamical systems.
• Systems of Differential Equations That are Competitive or Cooperative. IV: Structural Stability in Three-Dimensional Systems
• Systems of Differential Equations that are Competitive or Cooperative II: Convergence Almost Everywhere
• Systems of Differential Equations Which Are Competitive or Cooperative: I. Limit Sets
• Systems of differential equations that are competitive or cooperative. VI: A localC^rClosing Lemma for 3-dimensional systems
• From local to global behavior in competitive Lotka-Volterra systems
• Ann-dimensional competitive Lotka Volterra system is generically determined by the edges of its carrying simplex
• Generic Properties of Polynomial Vector Fields at Infinity
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in \(\mathbb{R}_+^4\)