Planar Kolmogorov Systems with Infinitely Many Singular Points at Infinity

被引：0

作者：

Diz-Pita, Erika ^{[1
]}

Llibre, Jaume ^{[2
]}

Victoria Otero-Espinar, M. ^{[1
]}

机构：

[1] Univ Santiago de Compostela, Dept Estat Anal Matemat & Optimizac, Santiago De Compostela 15705, Spain

[2] Univ Autonoma Barcelona, Dept Matemat, Barcelona 08193, Spain

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2022年 / 32卷 / 05期

基金：

欧盟地平线“2020”;

关键词：

Kolmogorov system; Lotka-Volterra system; phase portrait; Poincare disc; LOTKA-VOLTERRA SYSTEM; GLOBAL DYNAMICS;

D O I：

10.1142/S0218127422500651

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We classify the global dynamics of the five-parameter family of planar Kolmogorov systems (y)over dot = y(b(0) + b(1yz) + b(2y) + b(3z)), (z)over dot = z(c(0) + b(1yz) + b(2y) + b(3z)), which is obtained from the Lotka-Volterra systems of dimension three. These systems have infinitely many singular points at inifnity. We give the topological classification of their phase portraits in the Poincare disc, so we can describe the dynamics of these systems near infinity. We prove that these systems have 13 topologically distinct global phase portraits.

引用

页数：13