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arXiv · 1708.04818

Rate-induced tipping from periodic attractors: partial tipping and connecting orbits

Hassan M. Alkhayuon·Peter Ashwin
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Abstract

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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Hassan M. Alkhayuon, Peter Ashwin. 2017-08-16. Rate-induced tipping from periodic attractors: partial tipping and connecting orbits. https://doi.org/10.1063/1.5000418

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