周期吸引子的率诱导倾翻：部分倾翻和连接轨道
Rate-induced tipping from periodic attractors: partial tipping and connecting orbits
摘要：
我们考虑如何故障的准静态近似吸引子可以导致率引起的小费，在跟踪/小费行为的轨迹的定性变化，其特征在于在一个临界速率。与率引起的倾斜（其中跟踪的一个分支的准静态吸引子打破），我们发现一个新的现象，吸引子，而不是简单的平衡：部分倾斜的拉回吸引子的某些阶段的周期性吸引子尖端和其他跟踪的准静态吸引子。对于具有周期吸引子的两个渐近自治系统之间的参数移动的特定模型系统，我们将率诱导的临界值分解为部分临界值和完全临界值。我们发现，这些阈值可以发现在某些周期性（PtoP）和平衡（PtoE）的连接，我们确定使用林的方法的增强系统。
英文摘要：
We consider how breakdown of the quasistatic approximation for attractors can lead to rate-induced tipping, where a qualitative change in tracking/tipping behaviour of trajectories can be characterised in terms of a critical rate. Associated with rate-induced tipping (where tracking of a branch of quasistatic attractors breaks down) we find a new phenomenon for attractors that are not simply equilibria: partial tipping of the pullback attractor where certain phases of the periodic attractor tip and others track the quasistatic attractor. For a specific model system with a parameter shift between two asymptotically autonomous systems with periodic attractors we characterise thresholds of rate-induced tipping to partial and total tipping. We show these thresholds can be found in terms of certain periodic-to-periodic (PtoP) and periodic-to-equilibrium (PtoE) connections that we determine using Lin's method for an augmented system.
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