论文标题
通过渐近系列和类似梅尔尼科夫的方法估计速率引起的倾斜
Estimating rate-induced tipping via asymptotic series and a Melnikov-like method
论文作者
论文摘要
该论文介绍了渐近自主标量普通微分方程中速率引起的倾斜的研究。我们证明，在这种倾斜的情况下，一种解决方案，该解决方案限制了过去极限问题的双曲稳定平衡失去均匀的渐近稳定性，并与溶液相吻合，该解决方案限制了未来限制问题的双曲线不稳定平衡。我们使用渐近系列来近似此类溶液对，并通过仅使用在有限的时间间隔上计算的溶液来表征速率诱导的小费的发生。此外，我们表明，采用渐近系列的梅尔尼科夫启发方法可以渐近地近似临界点。
The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution which limits at a hyperbolic stable equilibrium of the past limit-problem loses uniform asymptotic stability and coincides with a solution which limits at a hyperbolic unstable equilibrium of the future limit-problem. We use asymptotic series to approximate such pairs of solutions and characterize the occurrence of a rate-induced tipping by using only solutions calculable on finite time intervals. Moreover, we show that a Melnikov-inspired method employing the asymptotic series allows to asymptotically approximate the tipping point.
