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Global bifurcations and multi-pulse orbits of a parametric excited system with autoparametric resonance

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Abstract

We consider an autoparametric system which consists of an oscillator coupled with a parametrically excited subsystem. The oscillator and the subsystem are in one-to-one internal resonance. The excited subsystem is in principal parametric resonance. The system contains the most general type of quadratic and cubic non-linearities. The method of second-order averaging is used to yield a set of autonomous equations of the second-order approximations to the parametric excited system with autoparametric resonance. The Shilnikov-type multi-pulse orbits and chaotic dynamics of the averaged equations are studied in detail. The global bifurcation analysis indicates that there exist the heteroclinic bifurcations and the Shilnikov-type multi-pulse homoclinic orbits in the averaged equations. The results obtained above mean the existence of amplitude-modulated chaos in the Smale horseshoe sense in the parametric excited system with autoparametric resonance. The Shilnikov-type multi-pulse chaotic motions of the parametric excited system with autoparametric resonance are also found by using numerical simulation.

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Authors and Affiliations

  1. College of Science, Chang’an University, Xi’an, 710064, People’s Republic of China

    Hongkui Chen

  2. Institute of Engineering Mechanics, Xi’an Jiaotong University, Xi’an, 710049, People’s Republic of China

    Hongkui Chen & Qingyu Xu

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  1. Hongkui Chen
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  2. Qingyu Xu
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Correspondence to Hongkui Chen.

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Chen, H., Xu, Q. Global bifurcations and multi-pulse orbits of a parametric excited system with autoparametric resonance. Nonlinear Dyn 65, 187–216 (2011). https://doi.org/10.1007/s11071-010-9883-3

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  • DOI: https://doi.org/10.1007/s11071-010-9883-3

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