Acta mathematica scientia,Series A ›› 2021, Vol. 41 ›› Issue (3): 783-796.

Previous Articles     Next Articles

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
  • 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)


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

CLC Number: 

  • O175