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The European Physical Journal Special Topics

, Volume 228, Issue 9, pp 1839–1854 | Cite as

Frequency-amplitude characteristics of periodic motions in a periodically forced van der Pol oscillator

  • Yeyin Xu
  • Albert C. J. LuoEmail author
Regular Article Topical issue
  • 15 Downloads
Part of the following topical collections:
  1. Periodic Motions and Chaos in Nonlinear Dynamical Systems

Abstract

In this paper, nonlinear frequency-amplitude characteristics of periodic motions in a periodically forced van der Pol oscillator are studied systematically. The periodic motions of the van der Pol oscillator are determined by the semi-analytical method, and the corresponding stability and bifurcation analysis is completed through the eigenvalue analysis. From the finite Fourier series analysis, the nonlinear frequency-amplitude characteristics of periodic motions are analyzed. From the frequency-amplitude analysis, the limit cycle of the van der Pol oscillator can be obtained analytically as excitation amplitude approach to zero, rather than numerically. For the van der Pol oscillator, most of periodic motions in the van der pol oscillator are symmetric. However, an asymmetric period-1 motion in the van der Pol oscillator is discovered. Thus a bifurcation tree of period-1 motion to chaos can be found.

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Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical and Industrial Engineering Southern Illinois University EdwardsvilleEdwardsvilleUSA

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