Rate-Induced Tipping and Saddle-Node Bifurcation for Quadratic Differential Equations with Nonautonomous Asymptotic Dynamics

DOI10.1137/20M1339003zbMath1468.34053arXiv2110.02608WikidataQ113779079 ScholiaQ113779079MaRDI QIDQ4983538

Carmen Núñez, Rafael Obaya, Martin Rasmussen, Iacopo P. Longo

Publication date: 20 April 2021

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2110.02608

zbMATH Keywords

pullback attractornonautonomous dynamical systemcritical transitionskew product flownonautonomous bifurcationpullback repellerrate-induced tipping

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Stability of solutions to ordinary differential equations (34D20) Asymptotic properties of solutions to ordinary differential equations (34D05) Attractors of solutions to ordinary differential equations (34D45) Dynamical aspects of attractors and their bifurcations (37G35) Nonautonomous smooth dynamical systems (37C60) Computational methods for attractors of dynamical systems (37M22)

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Cites Work

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• Nonautonomous linear Hamiltonian systems: oscillation, spectral theory and control
• Non-smooth saddle-node bifurcations. III: Strange attractors in continuous time.
• Minimal sets in monotone and concave skew-product semiflows. I: A general theory
• Nonautonomous saddle-node bifurcations: random and deterministic forcing
• Attractors for infinite-dimensional non-autonomous dynamical systems
• Nonautonomous continuation of bounded solutions
• Minimal sets in monotone and concave skew-product semiflows. II: Two-dimensional systems of differential equations
• Attractivity and bifurcation for nonautonomous dynamical systems
• A non-autonomous bifurcation theory for deterministic scalar differential equations
• Almost periodic differential equations
• Existence of dichotomies and invariant splittings for linear differential systems. II
• Dichotomies in stability theory
• Disconjugacy
• Excitability in ramped systems: the compost-bomb instability
• OLD AND NEW RESULTS ON STRANGE NONCHAOTIC ATTRACTORS
• The structure of the bounded trajectories set of a scalar convex differential equation
• Rate-induced tipping from periodic attractors: Partial tipping and connecting orbits
• Differential equations with limit-periodic forcings
• Compactification for asymptotically autonomous dynamical systems: theory, applications and invariant manifolds
• Basin bifurcations, oscillatory instability and rate-induced thresholds for Atlantic meridional overturning circulation in a global oceanic box model
• Parameter shifts for nonautonomous systems in low dimension: bifurcation- and rate-induced tipping