Multiple limit cycles and centers on center manifolds for Lorenz system

作者：Wang, Qinlong; Huang, Wentao^*; Feng, Jingjing

来源：Applied Mathematics and Computation, 2014, 238: 281-288.

DOI：10.1016/j.amc.2014.04.034

• Lorenz system
• Hopf bifurcation
• Center-focus
• Center manifold

For Lorenz system we investigate multiple Hopf bifurcation and centerfocus problem of its equilibria. By applying the method of symbolic computation, we obtain the first three singular point quantities. It is proven that Lorenz system can generate 3 small limit cycles from each of the two symmetric equilibria. Furthermore, the center conditions are found and as weak foci the highest order is proved to be the third, thus we obtain at most 6 small limit cycles from the symmetric equilibria via Hopf bifurcation. At the same time, we realize also that though the same for the related three-dimensional chaotic systems, Lorenz system differs in Hopf bifurcation greatly from the Chen system and Lu system.

• 出版日期2014-7-1
• 单位贺州学院; 长江大学; 桂林电子科技大学