Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System

Standard

Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System. / Wang, Fanrui; Liu, Ting; Kuznetsov, Nikolay V.; Wei, Zhouchao.

In: International Journal of Bifurcation and Chaos, Vol. 31, No. 05, 2150075, 04.2021.

Research output: Contribution to journal › Article › peer-review

Author

Wang, Fanrui ; Liu, Ting ; Kuznetsov, Nikolay V. ; Wei, Zhouchao. / Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System. In: International Journal of Bifurcation and Chaos. 2021 ; Vol. 31, No. 05.

BibTeX

@article{482cdf1fcf364374ac1e9e6c161ec737,

title = "Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System",

abstract = "In this paper, the Jacobi stability of a two-degree-of-freedom mechanical system is studied by the innovative application of KCC-theory, namely differential geometric methods. We discuss the Jacobi stability of two equilibria and a periodic orbit by constructing geometric invariants. Both the regions of Jacobi stability and Lyapunov stability are presented to show the difference. We draw the phase portraits of the deviation vector near two equilibria under specific parameter values and initial conditions, and point out the sensitivity of deviation vector to initial conditions. In addition, the corresponding instability exponent and curvature are applicable for predicting the onset of chaos, which help us to detect chaotic behaviors quantitatively. ",

keywords = "chaos, deviation, Jacobi stability, KCC-theory, mechanical system, DYNAMICS, KCC THEORY, DIFFERENTIAL GEOMETRIC STRUCTURE",

author = "Fanrui Wang and Ting Liu and Kuznetsov, {Nikolay V.} and Zhouchao Wei",

year = "2021",

month = apr,

doi = "10.1142/s0218127421500759",

language = "English",

volume = "31",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

number = "05",

}

RIS

TY - JOUR

T1 - Jacobi Stability Analysis and the Onset of Chaos in a Two-Degree-of-Freedom Mechanical System

AU - Wang, Fanrui

AU - Liu, Ting

AU - Kuznetsov, Nikolay V.

AU - Wei, Zhouchao

PY - 2021/4

Y1 - 2021/4

N2 - In this paper, the Jacobi stability of a two-degree-of-freedom mechanical system is studied by the innovative application of KCC-theory, namely differential geometric methods. We discuss the Jacobi stability of two equilibria and a periodic orbit by constructing geometric invariants. Both the regions of Jacobi stability and Lyapunov stability are presented to show the difference. We draw the phase portraits of the deviation vector near two equilibria under specific parameter values and initial conditions, and point out the sensitivity of deviation vector to initial conditions. In addition, the corresponding instability exponent and curvature are applicable for predicting the onset of chaos, which help us to detect chaotic behaviors quantitatively.

AB - In this paper, the Jacobi stability of a two-degree-of-freedom mechanical system is studied by the innovative application of KCC-theory, namely differential geometric methods. We discuss the Jacobi stability of two equilibria and a periodic orbit by constructing geometric invariants. Both the regions of Jacobi stability and Lyapunov stability are presented to show the difference. We draw the phase portraits of the deviation vector near two equilibria under specific parameter values and initial conditions, and point out the sensitivity of deviation vector to initial conditions. In addition, the corresponding instability exponent and curvature are applicable for predicting the onset of chaos, which help us to detect chaotic behaviors quantitatively.

KW - chaos

KW - deviation

KW - Jacobi stability

KW - KCC-theory

KW - mechanical system

KW - DYNAMICS

KW - KCC THEORY

KW - DIFFERENTIAL GEOMETRIC STRUCTURE

UR - http://www.scopus.com/inward/record.url?scp=85105554281&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/d80f2924-f23f-3ec9-8aca-bb694a6aaa29/

U2 - 10.1142/s0218127421500759

DO - 10.1142/s0218127421500759

M3 - Article

AN - SCOPUS:85105554281

VL - 31

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 05

M1 - 2150075

ER -

ID: 78768352