论文标题
Cubic Lotka-Volterra系统的可集成性和线性化条件
Integrability and linearizability conditions for a cubic Lotka-Volterra systems
论文作者
论文摘要
这项工作的主要目的是调查差异系统家族的起源的单个点周围的可集成性和线性性问题，特别是我们对（1：1：-1：1）共鸣的三维立方体Lotka-Volterra系统感兴趣。我们为可集成性和线性性问题提供了一套必要条件。两个独立第一积分的局部存在保证了这些条件也足够。此外，我们使用DARBOUX的集成性方法和其他一些技术来表明该系统在原点上允许两个独立的第一积分。
The main objective of this work is to investigate the integrability and linearizability problems around a singular point at the origin of the family of differential systems Particularly we are interested in the three-dimensional cubic Lotka-Volterra systems for (1:-1:1) resonant. We give a complete set of necessary conditions for both integrability and linearizability problems. The local existences of two independent first integrals guarantee that these conditions are sufficient as well. Furthermore, we use the Darboux method of integrability and some other techniques to show that the system admits two independent first integrals at the origin.
