Dynamical systems like the one described by the three-variable Lorenz-63 model may serve as metaphors for complex natural systems such as climate systems. When these systems are perturbed by external forcing factors, they tend to relax back to their equilibrium conditions after the forcing has shut off. Here we investigate the behavior of such transients in the Lorenz-63 model by studying its trajectories initialized far away from the asymptotic attractor. Counterintuitively, these transient trajectories exhibit complex routes and, in particular, the sensitivity to initial conditions is akin to that of the asymptotic behavior on the attractor. Thus, similar extreme events may lead to widely different variations before the perturbed system returns back to its statistical equilibrium.

中文翻译：

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Lorenz-63 模型作为气候瞬态复杂性的隐喻

像三变量 Lorenz-63 模型所描述的动力系统一样，可以作为气候系统等复杂自然系统的隐喻。当这些系统受到外部强迫因素的干扰时，它们往往会在强迫关闭后放松回到平衡状态。在这里，我们通过研究远离渐近吸引子初始化的轨迹来研究 Lorenz-63 模型中此类瞬变的行为。与直觉相反，这些瞬态轨迹表现出复杂的路线，特别是对初始条件的敏感性类似于吸引子上的渐近行为。因此，类似的极端事件可能会在扰动系统返回到其统计平衡之前导致大不相同的变化。