On Conditions for Rate-induced Tipping in Multi-dimensional Dynamical Systems
On Conditions for Rate-induced Tipping in Multi-dimensional Dynamical Systems
复制标题
多维动力系统中速率诱发倾翻的条件
DOI：
10.1007/s10884-019-09730-9
复制
发表时间：
2020
影响因子：
1.3
通讯作者：
Jones, Christopher K.
中科院分区：
文献类型：
--
作者：
Kiers, Claire;Jones, Christopher K.
在一维系统中，对远离吸引不动点的速率诱导倾转（r倾转）的可能性进行了深入的研究。在这些系统中，不可能有r倾倾偏离准稳定平衡路径，即正向盆地稳定（FBS），但对于某种类型的非盆地稳定路径，r倾倾是保证的。我们将研究这些结果是否适用于多维系统。特别地，我们将证明保证一维r倾翻的相同条件也保证高维r倾翻；然而，即使在二维系统中，r也有可能偏离FBS路径。我们将提出一个不同的条件，前向流入稳定性（FIS），我们证明它足以在所有维度上防止r倾翻。这种情况虽然很自然，但很难用具体的例子来证实。单调系统是一类FIS由一个容易验证的条件隐含的系统。因此，我们看到这些系统的附加结构如何以类似于一维的方式直接预测r倾斜的可能性。特别地，我们将证明单调系统中的FBS和FIS条件简化为比较平衡点随时间的相对位置。给出了一个单调系统的例子，演示了如何应用这些思想来准确地确定何时可能发生r倾翻。
The possibility ofrate-induced tipping(R-tipping) away from an attracting fixed point has been thoroughly explored in 1-dimensional systems. In these systems, it is impossible to have R-tipping away from a path of quasi-stable equilibria that isforward basin stable(FBS), but R-tipping is guaranteed for paths that are non-FBS of a certain type. We will investigate whether these results carry over to multi-dimensional systems. In particular, we will show that the same conditions guaranteeing R-tipping in 1-dimension also guarantee R-tipping in higher dimensions; however, it is possible to have R-tipping away from a path that is FBS even in 2-dimensional systems. We will propose a different condition,forward inflowing stability(FIS), which we show is sufficient to prevent R-tipping in all dimensions. The condition, while natural, is difficult to verify in concrete examples.Monotone systemsare a class for which FIS is implied by an easily verifiable condition. As a result, we see how the additional structure of these systems makes predicting the possibility of R-tipping straightforward in a fashion similar to 1-dimension. In particular, we will prove that the FBS and FIS conditions in monotone systems reduce to comparing the relative positions of equilibria over time. An example of a monotone system is given that demonstrates how these ideas are applied to determine exactly when R-tipping is possible.
影响因子：
1.7
作者：
Ashwin, Peter;Perryman, Clare;Wieczorek, Sebastian
通讯作者：
Wieczorek, Sebastian
洛伦兹系统向混沌过渡过程中相空间的全局组织
DOI：
--
发表时间：
2015
期刊：
影响因子：
--
作者：
E. Doedel;B. Krauskopf;H. Osinga
通讯作者：
H. Osinga