对准周期强迫的混沌和非混沌响应：由米兰科维奇强迫控制的冰河期可预报性的限制
Chaotic and non-chaotic response to quasiperiodic forcing: limits to predictability of ice ages paced by Milankovitch forcing
摘要：
众所周知，对一个非线性系统，即使是一个二维自治系统施加周期性的强迫，如果强迫引起相空间的充分拉伸和折叠，也会产生对初始条件敏感的混沌响应。准周期强迫同样可以产生混沌响应，其中改变参数时向混沌的过渡可以使系统进入奇怪的非混沌行为区域。虽然人们普遍认为更新世冰期的时间至少部分是由于米兰科维奇强迫（可以近似为准周期性的，能量集中在少数频率附近），但从强迫中可以推断出冰川和冰消时间的精确细节仍然不清楚。在本文中，我们进行了定量比较的几个低阶的非线性概念模型的响应，这些冰期的各种类型的准周期强迫。通过计算最大的李雅普诺夫指数和平均周期，我们表明，许多模型可以有一个混沌响应的准周期强迫的强迫幅度的范围内，即使一些最简单的概念模型没有。这些结果表明，冰河时代的步伐迫使可能只有有限的决定性。
英文摘要：
It is well known that periodic forcing of a nonlinear system, even of a two-dimensional autonomous system, can produce chaotic responses with sensitive dependence on initial conditions if the forcing induces sufficient stretching and folding of the phase space. Quasiperiodic forcing can similarly produce chaotic responses, where the transition to chaos on changing a parameter can bring the system into regions of strange non-chaotic behaviour. Although it is generally acknowledged that the timings of Pleistocene ice ages are at least partly due to Milankovitch forcing (which may be approximated as quasiperiodic, with energy concentrated near a small number of frequencies), the precise details of what can be inferred about the timings of glaciations and deglaciations from the forcing is still unclear. In this paper, we perform a quantitative comparison of the response of several low-order nonlinear conceptual models for these ice ages to various types of quasiperiodic forcing. By computing largest Lyapunov exponents and mean periods, we demonstrate that many models can have a chaotic response to quasiperiodic forcing for a range of forcing amplitudes, even though some of the simplest conceptual models do not. These results suggest that pacing of ice ages to forcing may have only limited determinism.
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