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A hyperbolic Lindstedt–Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators

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Abstract

A hyperbolic Lindstedt–Poincaré method is presented to determine the homoclinic solutions of a kind of nonlinear oscillators, in which critical value of the homoclinic bifurcation parameter can be determined. The generalized Liénard oscillator is studied in detail, and the present method’s predictions are compared with those of Runge– Kutta method to illustrate its accuracy.

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Authors and Affiliations

  1. Department of Applied Mechanics and Engineering, Sun Yat-sen University, 510275, Guangzhou, China

    Y. Y. Chen & S. H. Chen

  2. Department of Mechanical Engineering, The University of Hong Kong, Pokfulam, Hong Kong SAR, China

    Y. Y. Chen & K. Y. Sze

Authors
  1. Y. Y. Chen
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  2. S. H. Chen
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  3. K. Y. Sze
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Corresponding author

Correspondence to S. H. Chen.

Additional information

The project supported by the National Natural Science Foundation of China (10672193), Sun Yat-sen University (Fu Lan Scholarship) and the University of Hong Kong (CRGC grant).

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Chen, Y.Y., Chen, S.H. & Sze, K.Y. A hyperbolic Lindstedt–Poincaré method for homoclinic motion of a kind of strongly nonlinear autonomous oscillators. Acta Mech Sin 25, 721–729 (2009). https://doi.org/10.1007/s10409-009-0276-0

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  • DOI: https://doi.org/10.1007/s10409-009-0276-0

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