具有任意程度的广义波格丹诺夫-塔肯斯系统

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Bulletin des Sciences Mathematiques Pub Date : 2024-08-12 DOI:10.1016/j.bulsci.2024.103491

Hebai Chen , Dehong Dai , Yuhao Meng , Zhaoxia Wang

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引用次数: 0

摘要

本文旨在给出一个具有任意度的广义波格丹诺夫-塔肯斯系统的分岔图和泊恩卡雷圆盘上的所有全局相位肖像。此外，该系统还具有丰富的非线性现象，如双极限循环分岔、霍普夫分岔、同线性分岔、异线性分岔等。与经典的波格丹诺夫-塔肯斯系统相比，该系统的非线性现象更为丰富和复杂。

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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A generalized Bogdanov-Takens system with arbitrary degree

The aim of this paper is to give the bifurcation diagram and all global phase portraits in the Poincaré disc of a generalized Bogdanov-Takens system with arbitrary degree. Moreover, the system has abundant nonlinear phenomena, such as double limit cycle bifurcation, Hopf bifurcation, homoclinic bifurcation, heteroclinic bifurcation, and so on. Notice that the nonlinear phenomena of the system are more abundant and more complex than the classic Bogdanov-Takens system.

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