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### 高维多项式微分系统Zero-Hopf分岔分析及算法推导

1. 北京航空航天大学数学科学学院, 信息与行为教育部重点实验室, 北京 100191
• 收稿日期:2021-07-23 修回日期:2021-12-02 出版日期:2021-12-25 发布日期:2022-03-16
• 基金资助:
国家自然科学基金（12101032，11625105，12131004）资助课题.

HUANG Bo, HAN Deren. Analysis of Zero-Hopf Bifurcation in High Dimensional Polynomial Differential Systems with Algorithm Derivation[J]. Journal of Systems Science and Mathematical Sciences, 2021, 41(12): 3280-3298.

### Analysis of Zero-Hopf Bifurcation in High Dimensional Polynomial Differential Systems with Algorithm Derivation

HUANG Bo, HAN Deren

1. LMIB, School of Mathematical Sciences, Beihang University, Beijing 100191
• Received:2021-07-23 Revised:2021-12-02 Online:2021-12-25 Published:2022-03-16

This paper deals with the Zero-Hopf bifurcation in high dimensional polynomial differential systems. First, we reduce the problem of bifurcation analysis to an algebraic problem, and we give a method for determining the bifurcation set of the Zero-Hopf bifurcation points of differential systems by using symbolic algorithm for solving semi-algebraic systems. Then, based on the second order averaging method, the algorithmic framework of the Zero-Hopf bifurcation analysis of differential systems is derived, and the limit cycle bifurcation problem is studied through specific examples by using the methods of symbolic computation, and some new results are obtained. Finally, we propose several related research problems.

MR(2010)主题分类:

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