- About this Journal ·
- Abstracting and Indexing ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Recently Accepted Articles ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 813957, 6 pages
The Application of the Undetermined Fundamental Frequency Method on the Period-Doubling Bifurcation of the 3D Nonlinear System
1School of Mechanical Engineering, Tianjin Polytechnic University, Tianjin 300072, China
2Department of Mechanics, Tianjin University, Tianjin 300072, China
Received 28 April 2013; Revised 10 August 2013; Accepted 10 August 2013
Academic Editor: Ren Yong
Copyright © 2013 Gen Ge and Wei Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
- M. J. Feigenbaum, “The universal metric properties of nonlinear transformations,” Journal of Statistical Physics, vol. 21, no. 6, pp. 669–706, 1979.
- L. Q. Wang and M. T. Xu, “Property of period-doubling bifurcations,” Chaos, Solitons and Fractals, vol. 24, no. 2, pp. 527–532, 2005.
- D. W. Berns, J. L. Moiola, and G. R. Chen, “Detecting period-doubling bifurcation: an approximate monodromy matrix approach,” Automatica, vol. 37, no. 11, pp. 1787–1795, 2001.
- R. H. Rand, “Analytical approximation for period-doubling following a Hopf bifurcation,” Mechanics Research Communications, vol. 16, no. 2, pp. 117–123, 1989.
- M. Belhaq and M. Houssni, “Symmetry-breaking and first period-doubling following a Hopf bifurcation in a three-dimensional system,” Mechanics Research Communications, vol. 22, no. 3, pp. 221–231, 1995.
- M. Belhaq, E. Freire, M. Houssni, and A. J. Rodríguez-Luis, “Second period-doubling in a three-dimensional system,” Mechanics Research Communications, vol. 26, no. 2, pp. 123–128, 1999.
- A. Y. T. Leung and Q. C. Zhang, “Complex normal form for strongly non-linear vibration systems exemplified by Duffing-van der Pol equation,” Journal of Sound and Vibration, vol. 213, no. 5, pp. 907–914, 1998.
- Q. C. Zhang, W. Wang, and W. Y. Li, “Heteroclinic bifurcation of strongly nonlinear oscillator,” Chinese Physics Letters, vol. 25, no. 5, p. 1905, 2008.
- A. H. Nayfeh, Method of Normal Forms, John Wiley, New York, NY, USA, 1993.