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THE STRUCTURE OF ARNOLD TONGUE OVERLAPS IN DUFFING EQUATION WITHOUT SMALL PARAMETERS

YANBIN LIU

School of Astronautics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001, P. R. China

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YUSHU CHEN

School of Astronautics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001, P. R. China

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, and

QINGJIE CAO

School of Astronautics, Harbin Institute of Technology, P. O. Box 137, Harbin 150001, P. R. China

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https://doi.org/10.1142/S021812741102932XCited by:1 (Source: Crossref)

Abstract

Duffing equation is a representative nonlinear equation in practical engineering systems, where the most existing research focuses on local solutions of weakly nonlinear systems. In this paper, we study global bifurcations and chaos of the standard Duffing system by employing the Arnold tongue, and use the basin of attraction to investigate the properties of the Arnold tongue overlap. Our results show that a resonance solution and chaos could coexist, when the parameters are on the Arnold tongue overlap. The phenomenon does not exist in a system described by a weak Duffing equation. Numerical solutions for these bifurcations and chaos are also provided to demonstrate the theoretical results.

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