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.
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