论文标题
$（1：-3：1）的整体方面$ resonance lotka- volterra方程与非标准分析
Integral Aspects of $(1:-3:1)$ Resonance Lotka--Volterra Equations with Nonstandard Analysis
论文作者
论文摘要
在本文中，研究了具有$（δ：-3δ：δ）$ - 共振的可整合和可线化的Lotka-Volterra方程的问题。在$δ= 1 $且足够的情况下，这两个问题的必要条件均可获得。还表明，在某些情况下，非标准分析在证明足够的整合条件方面具有重要作用。非标准分析方法已用于给定系统的整体方面的扰动和不受干扰的情况。
In this paper the problems of integrable and linearizable Lotka-Volterra equations with $(δ:-3 δ:δ)$-resonance are studied. The necessary conditions for both problems are obtained in the case when $δ=1$ and it's sufficiency are proved. It is also shown that non-standard analysis has an important role in proving the sufficient integrable conditions in some cases. The non-standard analysis approaches have been used for both perturbed and unperturbed cases for integral aspects of the given system.
