混沌强迫海洋模型中危机的有限时间分析
Finite-Time Analysis of Crises in a Chaotically Forced Ocean Model
AI总结：
本研究耦合Stommel箱模型与Lorenz模型，分析混沌强迫下的危机现象，识别出新型消失盆地危机，并通过有限时间Lyapunov指数揭示危机与双曲性丧失的关联，且证明该行为具有普适性。
摘要：
我们考虑Stommel箱模型与Lorenz模型的耦合，旨在研究已知在足够强迫下发生的所谓“危机”。在此背景下，危机被表征为在临界强迫强度下混沌吸引子的破坏。我们记录了我们的模型中可能出现的各种混沌吸引子和危机，重点关注Lorenz模型始终混沌且Stommel箱模型存在双稳态的参数区域。边界危机中发生的混沌鞍碰撞被可视化，混沌鞍使用Saddle-Straddle算法计算。我们识别出一种新型的边界危机子类型，即消失盆地危机。对于超过危机的强迫强度，我们证明了持续混沌吸引子与混沌瞬态或幽灵吸引子（取决于边界危机的类型）之间合并的可能性。对危机强迫水平附近有限时间Lyapunov指数的研究揭示了两个近中性指数之间的收敛，特别是在轨迹对发散最敏感的点处。这表明与危机发生相关的双曲性丧失。最后，我们通过将Stommel箱模型与其他奇异吸引子耦合来推广我们的发现，从而表明这些行为是相当普遍和稳健的。
英文摘要：
We consider a coupling of the Stommel box model and the Lorenz model, with the goal of investigating the so-called "crises" that are known to occur given sufficient forcing. In this context, a crisis is characterized as the destruction of a chaotic attractor under a critical forcing strength. We document the variety of chaotic attractors and crises possible in our model, focusing on the parameter region where the Lorenz model is always chaotic and where bistability exists in the Stommel box model. The chaotic saddle collisions that occur in a boundary crisis are visualized, with the chaotic saddle computed using the Saddle-Straddle Algorithm. We identify a novel sub-type of boundary crisis, namely a vanishing basin crisis. For forcing strength beyond the crisis, we demonstrate the possibility of a merging between the persisting chaotic attractor and either a chaotic transient or a ghost attractor depending on the type of boundary crisis. An investigation of the finite-time Lyapunov exponents around crisis levels of forcing reveals a convergence between two near-neutral exponents, particularly at points of a trajectory most sensitive to divergence. This points to loss of hyperbolicity associated with crisis occurrence. Finally, we generalize our findings by coupling the Stommel box model to other strange attractors and thereby show that the behaviours are quite generic and robust.
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