Attractivity and Bifurcation for Nonautonomous Dynamical Systems

Rasmussen, Martin

doi:10.1007/978-3-540-71225-1

Cited by 15 publications

(1 citation statement)

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“…Pick any compact and convex set K that contains a neighbourhood of A −∞ . Applying Lemma 5.1(i) of Rasmussen 23 , means that for any T > 0 and ǫ > 0 there is a τ 0 < −T such that…”

Section: Let Us Denote Umentioning

confidence: 99%

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

Alkhayuon

Ashwin

2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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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“…Pick any compact and convex set K that contains a neighbourhood of A −∞ . Applying Lemma 5.1(i) of Rasmussen 23 , means that for any T > 0 and ǫ > 0 there is a τ 0 < −T such that…”

Section: Let Us Denote Umentioning

confidence: 99%