Periodic Solutions of Branched Space from Closed Orbits under Mixed Perturbations

Abstract

By combining the means of the center manifold theorem and Planar branching theory, this paper studies the sufficient conditions for general three-dimensional systems to branch out into spatial periodic solutions under mixed perturbations, and obtains two theorems for judging the periodic solutions of general three-dimensional systems branching out from closed orbits, which generalize the results of existing planar systems.