• 论文 •

### Rabinovich系统的Jacobi分析

1. 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 Liu1,*(),Qiujian Huang2

1. 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)

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.

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