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Bifurcation Trees of Period-1 Motion to Chaos in a Duffing Oscillator With Double-Well Potential

[+] Author Affiliations
Yu Guo

Midwestern State University, Wichita Falls, TX

Albert C. J. Luo

Southern Illinois University Edwardsville, Edwardsville, IL

Paper No. DETC2015-48104, pp. V006T10A060; 8 pages
doi:10.1115/DETC2015-48104
From:
  • ASME 2015 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 6: 11th International Conference on Multibody Systems, Nonlinear Dynamics, and Control
  • Boston, Massachusetts, USA, August 2–5, 2015
  • Conference Sponsors: Design Engineering Division, Computers and Information in Engineering Division
  • ISBN: 978-0-7918-5716-8
  • Copyright © 2015 by ASME

abstract

In this paper, periodic motions of a periodically forced Duffing oscillator with double-well potential are analytically predicted through implicit discrete mappings. The implicit discrete maps are obtained from discretization of differential equation of the Duffing oscillator. From mapping structures, bifurcation trees of periodic motions are predicted analytically, and the corresponding stability and bifurcation analysis are carried out through eigenvalue analysis. From the analytical prediction, numerical results of periodic motions are performed to verify the analytical prediction.

Copyright © 2015 by ASME
Topics: Bifurcation , Chaos

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