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Title of Journal: Nonlinear Dyn

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Abbravation: Nonlinear Dynamics

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Kluwer Academic Publishers

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DOI

10.1016/0034-5687(82)90123-2

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1573-269X

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Resonance and Bifurcation in a Nonlinear Duffing S

Authors: Xu Wei Li Ruihong Li Shuang
Publish Date: 2006/08/29
Volume: 46, Issue: 1-2, Pages: 211-221
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Abstract

The dynamic behaviors of twodegreeoffreedom Duffing system with cubic coupled terms are studied First the steadystate 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 symmetrybreaking perioddoubling 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 crosssection and phase portrait which are plotted to show the manifestation of coexisting periodic and chaotic attractors

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