Strange nonchaotic attractors in a nonsmooth dynamical system

Gaolei Li, Yuan Yue* (Corresponding Author), Jianhua Xie, Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

Strange nonchaotic attractors (SNAs) have fractal geometric structure, but are nonchaotic in the dynamical sense. Since Grebogi et al. discovered SNA in 1984, it has become one of the important topics in nonlinear dynamics. Now, the study of SNAs has been mainly confined to smooth dynamics with quasiperiodic excitation or random excitation. In this paper, we consider a class of single-degree-of-freedom gear dynamical system with quasiperiodic forcing. We show that the gear transmission system can be modeled as a three-dimensional piecewise linear system, which belongs to a typical class of nonsmooth system. We then show that SNAs do exist in such nonsmooth dynamical system with quasiperiodic force. The dynamical behavior of the nonsmooth system is analyzed as a parameter is varied. The dynamics is analyzed through phase diagrams and bifurcation diagrams, Lyapunov exponents, singular continuous power spectrum, phase sensitivity of time series and rational approximations.

Original languageEnglish
Article number104858
JournalCommunications in Nonlinear Science and Numerical Simulation
Volume78
Early online date12 Jun 2019
DOIs
Publication statusPublished - Nov 2019

Fingerprint

Strange attractor
Dynamical systems
Dynamical system
Gears
Excitation
Piecewise Linear Systems
Power spectrum
Fractals
Phase diagrams
Fractal Structure
Linear systems
Continuous Spectrum
Time series
Rational Approximation
Geometric Structure
Bifurcation Diagram
Power Spectrum
Dynamical Behavior
Lyapunov Exponent
Nonlinear Dynamics

Keywords

  • Lyapunov exponent
  • Nonsmooth dynamical system
  • Phase sensitive property
  • Strange nonchaotic attractors

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Strange nonchaotic attractors in a nonsmooth dynamical system. / Li, Gaolei; Yue, Yuan (Corresponding Author); Xie, Jianhua; Grebogi, Celso.

In: Communications in Nonlinear Science and Numerical Simulation, Vol. 78, 104858, 11.2019.

Research output: Contribution to journalArticle

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AU - Grebogi, Celso

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