Rabinovich系统的Jacobi分析

数学物理学报 ›› 2021, Vol. 41 ›› Issue (3): 783-796.

Rabinovich系统的Jacobi分析

刘永建^1,*(),黄秋健²

¹ 玉林师范学院广西高校复杂系统优化与大数据处理重点实验室广西玉林 537000
² 广西民族大学理学院 & 广西大学附属中学南宁 530006

收稿日期:2020-03-08 出版日期:2021-06-26 发布日期:2021-06-09
通讯作者: 刘永建 E-mail:liuyongjianmaths@126.com
基金资助:
国家自然科学基金(11961074);广西自然科学基金重点项目(2018GXNSFDA281028);广西高校高水平创新团队项目([2018]35);玉林师范学院高层次人才启动项目(G2019ZK51)

Jacobi Analysis of the Rabinovich System

Yongjian Liu^1,*(),Qiujian Huang²

¹ Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing, Yulin Normal University, Guangxi Yulin 537000
² College of Sciences, Guangxi University for Nationalities & High School Affiliated to Guangxi University, Nanning 530006

Received:2020-03-08 Online:2021-06-26 Published:2021-06-09
Contact: Yongjian Liu E-mail:liuyongjianmaths@126.com
Supported by:
the NSFC(11961074);the NSF of Guangxi Province(2018GXNSFDA281028);the High Level Innovation Team Program from Guangxi Higher Education Institutions of China([2018]35);the Senior Talent Research Foundation of Yulin Normal University(G2019ZK51)

摘要/Abstract

摘要：

该文运用微分几何技术开展三维微分系统的复杂性研究.基于Kosambi-Cartan-Chern（KCC）理论，从系统轨线的任意点出发，分析三维Rabinovich系统的Jacobi稳定性态，并给出系统所有平衡点的Jacobi稳定的条件；在获得系统平衡点附近偏离向量及其分量的时间演化的基础上，通过引入不稳定性指数和曲率，同时结合数值仿真对系统的混沌机理进行探讨性分析，数值结果有力地验证了已有的理论分析结果.

关键词: KCC理论, Jacobi稳定性, 偏离曲率张量, 平衡点, 混沌

Abstract:

In this paper, the differential geometry technique is used to study the complexity of the system. Jacobi stability of the three-dimensional Rabinovich system is analyzed from any point of trajectory of the system. Based on KCC-theory, the Jacobi stable conditions of all equilibrium points of the system are obtained. On the basis of obtaining the time evolution of the deviation vector and its components near the equilibrium points of the system, the instability exponent and curvature are introduced, and the chaos mechanism of the system is analyzed tentatively by combining numerical simulation. Numerical results validate the existing theoretical analysis results.

Key words: KCC theory, Jacobi stability, Deviation curvature tensor, Equilibrium point, Chaos

中图分类号:

O175

刘永建,黄秋健. Rabinovich系统的Jacobi分析[J]. 数学物理学报, 2021, 41(3): 783-796.

Yongjian Liu,Qiujian Huang. Jacobi Analysis of the Rabinovich System[J]. Acta mathematica scientia,Series A, 2021, 41(3): 783-796.

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