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Three-Dimensional Lotka–Volterra Systems with 3:−1:2-Resonance
Mediterranean Journal of Mathematics ( IF 1.1 ) Pub Date : 2021-06-11 , DOI: 10.1007/s00009-021-01809-2
Waleed Aziz , Colin Christopher , Jaume Llibre , Chara Pantazi

We study the local integrability at the origin of a nine-parameter family of three-dimensional Lotka–Volterra differential systems with (3:− 1:2)-resonance. We give necessary and sufficient conditions on the parameters of the family that guarantee the existence of two independent local first integrals at the origin of coordinates. Additionally, we classify those cases where the origin is linearizable.



中文翻译:

具有 3:−1:2 共振的三维 Lotka–Volterra 系统

我们研究了具有 (3:− 1:2) 共振的三维 Lotka-Volterra 微分系统的九参数族起源处的局部可积性。我们给出了保证在坐标原点存在两个独立的局部第一积分的族参数的充要条件。此外,我们对原点可线性化的情况进行分类。

更新日期:2021-06-13
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