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Chaos in the softening duffing system under multi-frequency periodic forces

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Abstract

The chaotic dynamics of the softening-spring Duffing system with multi-frequency external periodic forces is studied. It is found that the mechanism for chaos is the transverse heteroclinic tori. The Poincaré map, the stable and the unstable manifolds of the system under two incommensurate periodic forces were set up on a two-dimensional torus. Utilizing a global perturbation technique of Melnikov the criterion for the transverse interaction of the stable and the unstable manifolds was given. The system under more but finite incommensurate periodic forces was also studied. The Melnikov's global perturbation technique was therefore generalized to higher dimensional systems. The region in parameter space where chaotic dynamics may occur was given. It was also demonstrated that increasing the number of forcing frequencies will increase the area in parameter space where chaotic behavior can occur.

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Authors and Affiliations

  1. Institute of Noise & Vibration, Naval University of Engineering, 430033, Wuhan, PR China

    Lou Jing-jun Doctor, He Qi-wei Professor, Master & Zhu Shi-jian

Authors
  1. Lou Jing-jun Doctor
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  2. He Qi-wei Professor, Master
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  3. Zhu Shi-jian
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Correspondence to Zhu Shi-jian.

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Communicated by Chen Yu-shu

Biographies: Lou Jing-jun (1976≈) Zhu Shi-jian

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Jing-jun, L., Qi-wei, H. & Shi-jian, Z. Chaos in the softening duffing system under multi-frequency periodic forces. Appl Math Mech 25, 1421–1427 (2004). https://doi.org/10.1007/BF02438300

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  • DOI: https://doi.org/10.1007/BF02438300

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