Rate-induced tipping from periodic attractors: partial tipping and connecting orbits
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.
HA’s research is funded by the Higher Committee For Education Development in Iraq (HCED Iraq) grant agreement No D13436. PA’s research is partially supported by the CRITICS Innovative Training Network, funded by the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 643073.
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