Rabinovich系统的Jacobi分析

Abstract

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

CLC Number:

O175

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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Figures/Tables 10

References 38

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参数取值	平衡点	线性稳定性态	Jacobi稳定性态
$h = 5.5$	$S_0$	不稳定	不稳定
	$S_1, S_2$	不稳定	不稳定
$h = 6.75$	$S_0$	不稳定	不稳定
	$S_1, S_2$	不稳定	不稳定
$h = 10$	$S_0$	不稳定	不稳定
	$S_1, S_2$	不稳定	不稳定
$h = 15$	$S_0$	不稳定	不稳定
	$S_1, S_2$	不稳定	不稳定

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Jacobi Analysis of the Rabinovich System

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