Rate-induced tipping from periodic attractors: partial tipping and connecting orbits
Alkhayuon, HM; Ashwin, P
Date: 12 March 2018
Journal
Chaos
Publisher
AIP Publishing
Publisher DOI
Abstract
We consider how breakdown of the quasistatic approximation for attractors can lead to rate-dependent tipping, where a qualitative change in tracking/tipping behaviour of trajectories can be characterised in terms of a critical rate. Associated with rate-dependent tipping (where tracking of a branch of quasistatic attractors breaks down) ...
We consider how breakdown of the quasistatic approximation for attractors can lead to rate-dependent tipping, where a qualitative change in tracking/tipping behaviour of trajectories can be characterised in terms of a critical rate. Associated with rate-dependent 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-dependent 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.
Mathematics and Statistics
Faculty of Environment, Science and Economy
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