Chin. Phys. Lett.  2005, Vol. 22 Issue (11): 2780-2783    DOI:
Original Articles |
Limit Cycles near Stationary Points in the Lorenz System
YANG Shi-Pu;ZHU Ke-Qin;ZHOU Xiao-Zhou
Department of Engineering Mechanics, Tsinghua University, Beijing 100084
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YANG Shi-Pu, ZHU Ke-Qin, ZHOU Xiao-Zhou 2005 Chin. Phys. Lett. 22 2780-2783
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Abstract The limit cycles in the Lorenz system near the stationary points are analysed numerically. A plane in phase space of the linear Lorenz system is used to locate suitable initial points of trajectories near the limit cycles. The numerical results show a stable and an unstable limit cycle near the stationary point. The stable limit cycle is smaller than the unstable one and has not been previously reported in the literature. In addition, all the limit cycles in the Lorenz system are theoretically proven not to be planar.


Keywords: 05.45.Jn      05.45.Pq     
Published: 01 November 2005
PACS:  05.45.Jn (High-dimensional chaos)  
  05.45.Pq (Numerical simulations of chaotic systems)  
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https://cpl.iphy.ac.cn/       OR      https://cpl.iphy.ac.cn/Y2005/V22/I11/02780
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