Rabinovich系统的Jacobi分析  

Jacobi Analysis of the Rabinovich System

作　　者：刘永建[1] 黄秋健 Liu Yongjian;Huang Qiujian(Guangxi Colleges and Universities Key Laboratory of Complex System Optimization and Big Data Processing,Yulin Normal University,Guangxi Yulin 537000;College of Sciences,Guangxi University for Nationalities&High School Affiliated to Guangxi University,Nanning 530006)

机构地区：[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

出　　处：《数学物理学报（A辑）》2021年第3期783-796,共14页Acta Mathematica Scientia

基　　金：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)。

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.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.

关 键 词：KCC理论 Jacobi稳定性 偏离曲率张量 平衡点 混沌 

分 类 号：O175[理学—数学]