Rate-induced tipping from periodic attractors: partial tipping and connecting orbits
| Autor: | Alkhayuon, Hassan M., Ashwin, Peter |
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| Rok vydání: | 2017 |
| Předmět: | |
| Zdroj: | Chaos 28, 033608 (2018) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1063/1.5000418 |
| Popis: | 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. |
| Databáze: | arXiv |
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