二阶多项式微分抽动系统的零霍普夫分岔 ${\mathbb {R}^3}$

IF 0.7 3区数学 Q2 MATHEMATICS

Aequationes Mathematicae Pub Date : 2025-07-22 DOI:10.1007/s00010-025-01182-5

Jaume Llibre, Ammar Makhlouf

引用次数: 0

摘要

我们研究了${\mathbb {R}^3}$$$\begin{aligned} \begin{array}{l} \dot{x}=y,\\ \dot{y}=z,\\ \dot{z}=a_{0}+a_{1}x+a_{2}y+a_{3}z+a_{4}x^{2}+a_{5}xy+a_{6}xz+a_{7}y^{2}+a_{8}yz+a_{9}z^{2}, \end{array} \end{aligned}$$中所有二次多项式微分抽动系统的零hopf分岔，其中点表示对自变量t的导数，对于$k=0,1,...,9$，系数$a_{k}$是实数。

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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The Zero–Hopf bifurcations of the quadratic polynomial differential jerk systems in ${\mathbb {R}^3}$

We study the zero–Hopf bifurcations of all quadratic polynomial differential jerk systems in ${\mathbb {R}^3}$

$$\begin{aligned} \begin{array}{l} \dot{x}=y,\\ \dot{y}=z,\\ \dot{z}=a_{0}+a_{1}x+a_{2}y+a_{3}z+a_{4}x^{2}+a_{5}xy+a_{6}xz+a_{7}y^{2}+a_{8}yz+a_{9}z^{2}, \end{array} \end{aligned}$$

where the dot denotes derivative with respect to the independent variable t and the coefficients $a_{k}$, for $k=0,1,...,9$, are real.

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来源期刊

Aequationes Mathematicae MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.70

自引率

12.50%

发文量

审稿时长

>12 weeks

期刊介绍： aequationes mathematicae is an international journal of pure and applied mathematics, which emphasizes functional equations, dynamical systems, iteration theory, combinatorics, and geometry. The journal publishes research papers, reports of meetings, and bibliographies. High quality survey articles are an especially welcome feature. In addition, summaries of recent developments and research in the field are published rapidly.

二阶多项式微分抽动系统的零霍普夫分岔 \({\mathbb {R}^3}\)

摘要