We demonstrate in this paper a new chaotic behavior in the Lorenz system with periodically excited parameters. We focus on the parameters with which the Lorenz system has only two asymptotically stable equilibrium points, a saddle and no chaotic dynamics. A new mechanism of generating chaos in the periodically excited Lorenz system is demonstrated by showing that some trajectories can visit different attractor basins due to the periodic variations of the attractor basins of the time-varying stable equilibrium points when a parameter of the Lorenz system is varying periodically.

中文翻译：

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周期性参数激发 Lorenz 系统中的混沌

我们在本文中展示了具有周期性激发参数的 Lorenz 系统中的一种新的混沌行为。我们专注于洛伦兹系统只有两个渐近稳定平衡点的参数，一个鞍座和无混沌动力学。证明了在周期性激发的洛伦兹系统中产生混沌的新机制：当洛伦兹系统的参数变化时，由于时变稳定平衡点的吸引子盆地的周期性变化，一些轨迹可以访问不同的吸引子盆地定期。