Abstract
In this paper, the sufficient condition for the existence of periodic solution of a class of three dimensional nonlinear dynamical systems is investigated. The moving Frenet frame is established on the closed orbit and the successor functions near the closed orbit are defined. According to the study of the existence of solution of the equation which obtained from the successor functions with the implicit function theorem, the sufficient condition for the existence of periodic solution of these systems is obtained. The results in this paper have important significance to decide the existence of periodic solution of three dimensional nonlinear dynamical systems.
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