Abstract
The limit cycles in the Lorenz system near the stationary points areanalysed numerically. A plane in phase space of the linear Lorenzsystem is used to locate suitable initial points of trajectories nearthe limit cycles. The numerical results show a stable and an unstablelimit cycle near the stationary point. The stable limit cycle issmaller than the unstable one and has not been previously reported inthe literature. In addition, all the limit cycles in the Lorenz systemare theoretically proven not to be planar.
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