A two-dimensional Kolmogorov system depending on two independent parameters and having a degenerate condition is studied in this work. We obtain local analytical properties of the system when the parameters vary in a sufficiently small neighborhood of the origin. The behavior of the system is described by bifurcation diagrams. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.

中文翻译：

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一类Kolmogorov系统的分析

在这项工作中研究了二维Kolmogorov系统，该系统取决于两个独立的参数并具有简并的条件。当参数在原点的足够小的邻域中变化时，我们获得系统的局部分析性质。系统的行为由分叉图描述。特别是在生物学和生态学中模拟种群动态时，可以找到Kolmogorov系统的应用。