Tipping mechanisms in a carbon cycle model.

IF 2.7 2区 数学 Q1 MATHEMATICS, APPLIED
Chaos Pub Date : 2025-05-01 DOI:10.1063/5.0241550
Katherine Slyman, Emmanuel Fleurantin, Christopher K R T Jones
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引用次数: 0

Abstract

Rate-induced tipping (R-tipping) occurs when a ramp parameter changes rapidly enough to cause the system to tip between co-existing, attracting states, while noise-induced tipping (N-tipping) occurs when there are random transitions between two attractors of the underlying deterministic system. This work investigates R-tipping and N-tipping events in a carbonate system in the upper ocean, in which the key objective is understanding how the system undergoes tipping away from a stable fixed point in a bistable regime. While R-tipping away from the fixed point fits the framework of an established scenario, N-tipping poses challenges due to a periodic orbit forming the basin boundary for the attracting fixed point of the underlying deterministic system. Furthermore, for N-tipping, we are interested in the situation where noise is away from the small noise limit as it is more appropriate for the application. We postulate that two key points on the basin boundary are critical to understanding the noisy behavior: the exit point of what we find to be the most probable escape path (MPEP), which is determined by the Onsager-Machlup functional, and the pivot point, a point identified through the Maslov index, which appears as an obstacle to the movement of the escape region of noisy trajectories through the periodic orbit as noise increases.

碳循环模型中的引爆机制。
当斜坡参数变化足够快,导致系统在共存的吸引状态之间倾斜时,就会发生速率诱导倾斜(r -倾斜),而当潜在确定性系统的两个吸引子之间存在随机转变时,就会发生噪声诱导倾斜(n -倾斜)。这项工作研究了上层海洋碳酸盐系统中的r倾翻和n倾翻事件,其中的关键目标是了解系统如何在双稳态状态下从稳定的固定点倾斜。远离固定点的r倾转符合既定情景的框架,而n倾转则面临挑战,因为周期轨道形成了潜在确定性系统吸引固定点的盆地边界。此外,对于N-tipping,我们感兴趣的是噪声远离小噪声限制的情况,因为它更适合应用。我们假设盆地边界上的两个关键点对于理解噪声行为至关重要:我们发现的最可能逃逸路径(MPEP)的出口点(由Onsager-Machlup泛函数确定)和枢轴点(通过马斯洛夫指数确定的点),随着噪声的增加,它似乎是噪声轨迹逃逸区域在周期轨道上运动的障碍。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Chaos
Chaos 物理-物理:数学物理
CiteScore
5.20
自引率
13.80%
发文量
448
审稿时长
2.3 months
期刊介绍: Chaos: An Interdisciplinary Journal of Nonlinear Science is a peer-reviewed journal devoted to increasing the understanding of nonlinear phenomena and describing the manifestations in a manner comprehensible to researchers from a broad spectrum of disciplines.
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