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- Title
Physical invariant measures and tipping probabilities for chaotic attractors of asymptotically autonomous systems.
- Authors
Ashwin, Peter; Newman, Julian
- Abstract
Physical measures are invariant measures that characterise "typical" behaviour of trajectories started in the basin of chaotic attractors for autonomous dynamical systems. In this paper, we make some steps towards extending this notion to more general nonautonomous (time-dependent) dynamical systems. There are barriers to doing this in general in a physically meaningful way, but for systems that have autonomous limits, one can define a physical measure in relation to the physical measure in the past limit. We use this to understand cases where rate-dependent tipping between chaotic attractors can be quantified in terms of "tipping probabilities". We demonstrate this for two examples of perturbed systems with multiple attractors undergoing a parameter shift. The first is a double-scroll system of Chua et al., and the second is a Stommel model forced by Lorenz chaos.
- Subjects
INVARIANT measures; ATTRACTORS (Mathematics); LORENZ equations; DYNAMICAL systems; PROBABILITY measures
- Publication
European Physical Journal: Special Topics, 2021, Vol 230, Issue 16/17, p3235
- ISSN
1951-6355
- Publication type
Article
- DOI
10.1140/epjs/s11734-021-00114-z