Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774336 | Journal of Differential Equations | 2017 | 23 Pages |
Abstract
In this paper we first give the sufficient and necessary conditions in order that two classes of polynomial Kolmogorov systems in R+4 are Hamiltonian systems. Then we study the integrability of these Hamiltonian systems in the Liouville sense. Finally, we investigate the global dynamics of the completely integrable Lotka-Volterra Hamiltonian systems in R+4. As an application of the invariant subsets of these systems, we obtain topological classifications of the 3-submanifolds in R+4 defined by the hypersurfaces axy+bzw+cx2y+dxy2+ez2w+fzw2=h, where a,b,c,d,e,f,w and h are real constants.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Jaume Llibre, Dongmei Xiao,