A 3D competitive Lotka-Volterra system with three limit cycles: A falsification of a conjecture by Hofbauer and So

被引：49

作者：

Gyllenberg, M

Yan, P ^{[1
]}

Wang, Y

机构：

[1] Univ Turku, Dept Math, FIN-20014 Turku, Finland

[2] Univ Helsinki, Dept Math & Stat, Rolf Nevanlinna Inst, FIN-00014 Helsinki, Finland

来源：

APPLIED MATHEMATICS LETTERS | 2006年 / 19卷 / 01期

基金：

芬兰科学院;

关键词：

competitive; Lotka-Volterra system; limit cycles; carrying simplex; Hopf bifurcation;

D O I：

10.1016/j.aml.2005.01.002

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For three-dimensional competitive Lotka-Volterra systems, Zeeman [M.L. Zeeman, Hopf bifurcations in competitive three-dimensional Lotka-Volterra systems, Dyn. Stab. Syst. 8 (1993) 189-217] identified 33 stable nullcline equivalence classes. Among these, only classes 26-31 may have limit cycles. Hofbauer and So [J. Hofbauer, J.W.-H. So, Multiple limit cycles for three dimensional Lotka-Volterra equations, Appl. Math. Lett. 7 (1994) 65-70] conjectured that the number of limit cycles is at most two for these systems. In this paper, we construct three limit cycles for class 29 without a heteroclinic polycycle in Zeeman's classification. (C) 2005 Elsevier Ltd. All rights reserved.

引用

页码：1 / 7

页数：7

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