Parameter shifts for nonautonomous systems in low dimension: bifurcation-and rate-induced tipping
Parameter shifts for nonautonomous systems in low dimension: bifurcation-and rate-induced tipping
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DOI：
10.1088/1361-6544/aa675b
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发表时间：
2017-06-01
期刊：
影响因子：
1.7
通讯作者：
Wieczorek, Sebastian
中科院分区：
文献类型：
--
作者：
Ashwin, Peter;Perryman, Clare;Wieczorek, Sebastian
我们讨论了非自治系统的不可逆倾翻的非线性现象，其中时变输入对应于从一个渐近值到另一个渐近值的平滑“参数移位”。我们表示小费的本地拉回吸引子的性质，并提出了一些结果如何非平凡的动态非自治系统可以推导出相关的自治系统的参数是固定的分岔图分析。特别是，我们表明，有一个独特的本地拉回点吸引子与每个线性稳定平衡的过去的限制。如果在参数偏移的值的范围内存在平衡的平滑稳定分支，则对于足够小的速率，拉回吸引子将保持接近（跟踪）该分支，尽管较大的速率可能导致速率诱导的翻转。更一般地说，我们可以跟踪某些稳定的路径，去沿着几个稳定的分支系统的伪轨道，足够小的速率。对于这些局部拉回点吸引子，我们定义了非自治系统的分岔诱导和不可逆率诱导的临界点的概念。在一维中，我们引入了前向盆地稳定性的概念，并使用它来给出一些充分条件的存在或不存在率引起的倾斜。我们应用我们的研究结果给出了一个概念性气候模型中不可逆转的利率引起的小费的标准。
We discuss the nonlinear phenomena of irreversible tipping for nonautonomous systems where time-varying inputs correspond to a smooth ` parameter shift' from one asymptotic value to another. We express tipping in terms of properties of local pullback attractors and present some results on how nontrivial dynamics for non-autonomous systems can be deduced from analysis of the bifurcation diagram for an associated autonomous system where parameters are fixed. In particular, we show that there is a unique local pullback point attractor associated with each linearly stable equilibrium for the past limit. If there is a smooth stable branch of equilibria over the range of values of the parameter shift, the pullback attractor will remain close to (track) this branch for small enough rates, though larger rates may lead to rate-induced tipping. More generally, we show that one can track certain stable paths that go along several stable branches by pseudo-orbits of the system, for small enough rates. For these local pullback point attractors, we define notions of bifurcation-induced and irreversible rate-induced tipping of the non-autonomous system. In one-dimension, we introduce the notion of forward basin stability and use this to give a number of sufficient conditions for the presence or absence of rate-induced tipping. We apply our results to give criteria for irreversible rate-induced tipping in a conceptual climate model.