Dynamics, integrability and topology for some classes of Kolmogorov Hamiltonian systems in

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• 作者：Jaume Llibre^a ; ^b ; ^{jllibre@mat.uab.cat} ; Dongmei Xiao^b ; ^{xiaodm@sjtu.edu.cn}
• 关键词：37K10 ; 37C27 ; 37K05
• 刊名：Journal of Differential Equations
• 出版年：2017
• 出版时间：5 February 2017
• 年：2017
• 卷：262
• 期：3
• 页码：2231-2253
• 全文大小：678 K
• 卷排序：262

文摘

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=haxy+bzw+cx2y+dxy2+ez2w+fzw2=h, where a,b,c,d,e,f,wa,b,c,d,e,f,w and h are real constants.