The third order melnikov function of a cubic integrable system under quadratic perturbations

被引：5
|
作者：
Asheghi, R. [1 ]
Nabavi, A. [1 ]
机构：
[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran
来源：
CHAOS SOLITONS & FRACTALS | 2020年 / 139卷
关键词：
Melnikov functions; Integrable system; Quadratic perturbations; Limit cycles; Reversible; LIMIT-CYCLES;
D O I：
10.1016/j.chaos.2020.110291
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this work, we consider a cubic integrable system under quadratic perturbations. We then study the limit cycles of the perturbed system by using Melnikov functions up to order three. We prove that the sharp upper bound of the number of limit cycles lies between six and seven. Also, we give an example that shows six limit cycles. (C) 2020 Elsevier Ltd. All rights reserved.
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页数：9
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