NDLI: Resonance and Bifurcation in a Nonlinear Duffing System with Cubic Coupled Terms

Content Provider	Springer Nature Link
Author	Wei, Xu Ruihong, Li Shuang, Li
Copyright Year	2006
Abstract	The dynamic behaviors of two-degree-of-freedom Duffing system with cubic coupled terms are studied. First, the steady-state responses in principal resonance and internal resonance of the system are analyzed by the multiple scales method. Then, the bifurcation structure is investigated as a function of the strength of the driving force F. In addition to the familiar routes to chaos already encountered in unidimensional Duffing oscillators, this model exhibits symmetry-breaking, period-doubling of both types and a great deal of highly periodic motion and Hopf bifurcation, many of which occur more than once. We explore the chaotic behaviors of our model using three indicators, namely the top Lyapunov exponent, Poincaré cross-section and phase portrait, which are plotted to show the manifestation of coexisting periodic and chaotic attractors.
Starting Page	211
Ending Page	221
Page Count	11
File Format	PDF
ISSN	0924090X
Journal	Nonlinear Dynamics
Volume Number	46
Issue Number	1-2
e-ISSN	1573269X
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2006-08-29
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	cubic coupled terms multiple scales method principal resonance internal resonance bifurcation chaos the top Lyapunov exponent
Content Type	Text
Resource Type	Article
Subject	Ocean Engineering Applied Mathematics Control and Systems Engineering Mechanical Engineering Electrical and Electronic Engineering Aerospace Engineering

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