A Perturbation Procedure for Limit Cycle and Heteroclinic Connection Analysis of Certain Self-Excited Oscillator

Abstract:

A perturbation procedure, in which the elliptic perturbation method and the hyperbolic perturbation method are applied, is presented for predicting heteroclinic connection of limit cycle or self-excited ocsillator. The limit cycle can be analytically　constructed first by the elliptic perturbation method after Hopf bifurcation, in which the amplitude of limit cycle can be　controlled by the modulus of elliptic functions. The heteroclinic trajectories, which are formed by the heteroclinic connection of limit cycle, can also be constructed by similar perturbation　procedure but adopting the hyperbolic functions instead of　elliptic functions. And the criterion of heteroclinic connection is given in the perturbation procedure. A typical self-excited oscillator is studied in detail to assess the present method.

• Periodical: Applied Mechanics and Materials (Volumes 204-208)
• Pages: 4529-4532
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.204-208.4529
• Online since: October 2012
• Authors: Yang Yang Chen, Wei Zhao, Le Wei Yan
• Keywords: Elliptic Perturbation Method, Heteroclinic Connection, Hyperbolic Perturbation Method, Limit Cycle

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