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Investigation of the Transition Character for Duffing System by Employing Periodicity Ratio and Lyapunov Exponents

[+] Author Affiliations
Lu Han, Liming Dai

University of Regina, Regina, SK, Canada

Huayong Zhang

North China Electric Power University, Beijing, P.R. China

Paper No. IMECE2010-37041, pp. 217-222; 6 pages
  • ASME 2010 International Mechanical Engineering Congress and Exposition
  • Volume 8: Dynamic Systems and Control, Parts A and B
  • Vancouver, British Columbia, Canada, November 12–18, 2010
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-4445-8
  • Copyright © 2010 by ASME


The transition characters from periodicity to chaos and periodicity to quasi-periodicity have been detected for a Duffing equation which is a representative nonlinear dynamic system who has complicated, diverse transition characters. Specifically, Lyapunov exponents and periodicity ratio method are both employed to diagnose the transition routes. By combining the two methods together, it is very efficient to classify different types of transition of a nonlinear differential system. It can be found that the transition routes from periodicity to chaos can be more divergent than other routes from periodicity to quasi-periodicity. Therefore, some predications can be made about the occurrence of the chaos by observing the divergence or convergence of the transition routes. Further more, the new symmetrical transition characters from periodicity to quasi-periodicity can be displayed in terms of the periodicity Ratio. Comparing to Lyapunov Exponents, the Periodicity Ratio can disclose more detailed transition information.

Copyright © 2010 by ASME



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