LIMIT CYCLE BIFURCATIONS OF A PLANAR NEAR-INTEGRABLE SYSTEM WITH TWO SMALL PARAMETERS

• 作者: Feng LIANG Maoan HAN Chaoyuan JIANG
• 来源期刊: 数学物理学报（英文版）
• 年，卷（期）: 2021,（4）
• 页码范围: 1034-1056
• 页数: 23页
• 语种: 英文
• DOI: 10.3969/j.issn.0252-9602.2021.04.002

摘要

In this paper we consider a class of polynomial planar system with two small parameters,ε and λ,satisfying 0 ＜ ε ＜＜ λ ＜＜ 1.The corresponding first order Melnikov function M1 with respect to ε depends on λ so that it has an expansion of the form M1 (h,λ) =∞∑k=0 M1k(h)λk.Assume that M1k'(h) is the first non-zero coefficient in the expansion.Then by estimating the number of zeros of M1k'(h),we give a lower bound of the maximal number of limit cycles emerging from the period annulus of the unperturbed system for 0 ＜ ε ＜＜ λ ＜＜ 1,when k'=0 or 1.In addition,for each k ∈ N,an upper bound of the maximal number of zeros of M1k(h),taking into account their multiplicities,is presented.