The Classification on the Global Phase Portraits of Two-dimensional Lotka¨CVolterra System

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• 作者：Feng Cao and Jifa Jiang
• 关键词：Finite critical point ; Infinite critical point ; Closed orbit ; Global phase portrait
• 刊名：Journal of Dynamics and Differential Equations
• 出版年：2008
• 出版时间：December, 2008
• 年：2008
• 卷：20
• 期：4
• 页码：797-830
• 全文大小：1.2 MB

文摘

This paper provides a complete classification on the global phase portraits of quadratic Lotka–Volterra system [(x)\dot]=x(a₀+a₁x+a₂y), [(y)\dot]=y(b₀+b₁x+b₂y){\dot{x}=x(a_{0}+a_{1}x+a_{2}y),\, \dot{y}=y(b_{0}+b_{1}x+b_{2}y)} . There are 143 different global phase portraits in the Poincar¨¦ disc up to a reversal of sense of all orbits. Firstly the sufficient and necessary conditions of the system with closed orbits are given. Then the properties on infinite and finite critical points are discussed. All global phase portraits are finally classified by combining all local information.