Comparison of the Hyperbolic Perturbation Method and the Hyperbolic Lindstedt-Poincaré Method for Homoclinic Solutions of Self-Excited Systems

Abstract:

The comparison of the hyperbolic perturbation method and the hyperbolic Lindstedt-Poincaré method for homoclinic solutions of self-excited systems is studied in this paper. The homoclinic solution of a generalized Van del Pol system with strongly quadratic nonlinearity is analytically derived by both of the methods. The critical value of the bifurcation parameter under which homoclinic trajectory forms can be determined by the both of the perturbation procedures. Typical numerical examples are studied in detail and compared to illustrate the accuracy and the efficiency.

• Periodical: Applied Mechanics and Materials (Volume 203)
• Pages: 411-415
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.203.411
• Online since: October 2012
• Authors: Yang Yang Chen, Le Wei Yan, Wei Zhao
• Keywords: Homoclinic Solution, Hyperbolic Lindstedt-Poincaré Method, Hyperbolic Perturbation Method, Self-Excited System

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