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 and periodic-to-equilibrium connections that we determine using Lin's method for an augmented system.
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Research Article| March 12 2018
Rate-induced tipping from periodic attractors: Partial tipping and connecting orbits
Special Collection: Multistability and Tipping
Hassan M. Alkhayuon;
Hassan M. Alkhayuon, Peter Ashwin; Rate-induced tipping from periodic attractors: Partial tipping and connecting orbits. Chaos 1 March 2018; 28 (3): 033608. https://doi.org/10.1063/1.5000418
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