Abstract
© 2016 Elsevier Inc. 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.
Original language | English |
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Pages (from-to) | 2231-2253 |
Journal | Journal of Differential Equations |
Volume | 262 |
Issue number | 3 |
DOIs | |
Publication status | Published - 5 Feb 2017 |
Keywords
- Global dynamics
- Hamiltonian system
- Hypersurfaces
- Liouvillian integrability
- Topological classification