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ANALYTICAL DYNAMICS OF PERIOD-m FLOWS AND CHAOS IN NONLINEAR SYSTEMS.
- Source :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering; Apr2012, Vol. 22 Issue 4, p1250093-1-1250093-29, 29p, 8 Charts, 10 Graphs
- Publication Year :
- 2012
-
Abstract
- In this paper, the analytical solutions for period-m flows and chaos in nonlinear dynamical systems are presented through the generalized harmonic balance method. The nonlinear damping, periodically forced, Duffing oscillator was investigated as an example to demonstrate the analytical solutions of periodic motions and chaos. Through this investigation, the mechanism for a period-m motion jumping to another period-n motion in numerical computation is found. In this problem, the Hopf bifurcation of periodic motions is equivalent to the period-doubling bifurcation via Poincare mappings of dynamical systems. The stable and unstable period-m motions can be obtained analytically. Even more, the stable and unstable chaotic motions can be achieved analytically. The methodology presented in this paper can be applied to other nonlinear vibration systems, which is independent of small parameters. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02181274
- Volume :
- 22
- Issue :
- 4
- Database :
- Complementary Index
- Journal :
- International Journal of Bifurcation & Chaos in Applied Sciences & Engineering
- Publication Type :
- Academic Journal
- Accession number :
- 75396647
- Full Text :
- https://doi.org/10.1142/S0218127412500939