In this paper, we perform a careful analysis of the forced PP04 model for climate change, in particular the behaviour of the ice ages. This system models the transition from a glacial to an inter-glacial state through a sudden release of oceanic carbon dioxide into the atmosphere. This process can be cast in terms of a Filippov dynamical system, with a discontinuous change in its dynamics related to the carbon dioxide release. By using techniques from the theory of non-smooth dynamical systems, we give an analysis of this model in the cases of both no insolation forcing and also periodic insolation forcing. This reveals a rich, and novel, dynamical structure to the solutions of the PP04 model. In particular, we see synchronized periodic solutions with subtle regions of existence which depend on the amplitude and frequency of the forcing. The orbits can be created/destroyed in both smooth and discontinuity-induced bifurcations. We study both the orbits and the transitions between them and make comparisons with actual climate dynamics.

中文翻译：

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基于非光滑动力系统理论的周期性强迫PP04气候模型分析

在本文中，我们对用于气候变化的强制PP04模型进行了仔细的分析，尤其是冰河时期的行为。该系统通过将海洋二氧化碳突然释放到大气中来模拟从冰川状态到冰川间状态的转变。可以根据Filippov动力学系统进行此过程，其动力学过程与二氧化碳释放相关的变化不连续。通过使用非光滑动力系统理论的技术，我们在无日照强迫和周期性日照强迫的情况下对该模型进行了分析。这揭示了PP04模型解决方案的丰富而新颖的动态结构。特别是，我们看到了同步周期解，其存在的细微区域取决于强迫的幅度和频率。轨道可以在光滑的和不连续的分叉中创建/销毁。我们研究了轨道及其之间的过渡，并与实际的气候动力学进行了比较。