一类片断平稳近哈密尔顿系统中的霍普夫分岔

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2024-07-24 DOI:10.1016/j.bulsci.2024.103471

Maoan Han, Shanshan Liu

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引用次数: 0

摘要

本文讨论了以抛物线-抛物线（PP）或焦点-抛物线（FP）类型为中心的平面片断平滑近哈密尔顿系统的霍普夫分岔。通过研究一阶梅利尼科夫函数的渐近展开，我们分别得到了这两种类型中心附近极限循环次数的上限和下限定理。最后，我们提供了两个应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Hopf bifurcation in a class of piecewise smooth near-Hamiltonian systems

In this paper, we discuss Hopf bifurcation for planar piecewise smooth near-Hamiltonian systems with a center of parabolic-parabolic (PP) or focus-parabolic (FP) type. By studying asymptotic expansion of the first order Melnikov function, we obtain theorems to find an upper bound and a lower bound of the number of limit cycles near the center of these two types, respectively. Finally we provide two applications.

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