Twelve limit cycles around a singular point in a planar cubic-degree polynomial system

被引：42

作者：

Yu, Pei ^{[1
]}

Tian, Yun ^{[1
]}

机构：

[1] Univ Western Ontario, Dept Appl Math, London, ON N6A 5B7, Canada

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2014年 / 19卷 / 08期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Hilbert's 16th problem; Cubic planar system; Center; Limit cycle; Bifurcation; Focus value; BIFURCATIONS; COMPUTATION;

D O I：

10.1016/j.cnsns.2013.12.014

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we prove the existence of 12 small-amplitude limit cycles around a singular point in a planar cubic-degree polynomial system. Based on two previously developed cubic systems in the literature, which have been proved to exhibit 11 small-amplitude limit cycles, we applied a different method to show 11 limit cycles. Moreover, we show that one of the systems can actually have 12 small-amplitude limit cycles around a singular point. This is the best result so far obtained in cubic planar vector fields around a singular point. (C) 2013 Elsevier B. V. All rights reserved.

引用

页码：2690 / 2705

页数：16

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