CLOSED ORBITS IN THE GENERAL LORENZ FAMILY

Abstract

This paper proves that all the closed orbits (including limit cycles) of the general Lorenz family must be planar, but only to be curves in space based on the technique of classification and identification for the quadratic surface in three-dimensional space. This result indicates that the qualitative property of the closed orbit for the systems is very complicated. We hope that this study would be beneficial for further studies of the dynamically rich chaotic system.