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math.DS2026
Early warnings of critical transitions through vector autoregression: lessons from multiscale systems
Bryony Hobden, Paul Ritchie, Peter Ashwin
In a nonautonomous nonlinear dynamical system, generic critical transitions (tipping points) are not limited to slow passage through fold bifurcations. They can also correspond to…
math.DS2025
Attracting measures
Julian Newman, Peter Ashwin
Under mild assumptions, the SRB measure associated to an Axiom A attractor has the following properties: (i) the empirical measure starting at a typical point near con…
math.DS2024
Internal noise interference to warnings of tipping points in generic multi-dimensional dynamical systems
Andreas Morr, Niklas Boers, Peter Ashwin
A deterministic dynamical system that slowly passes through a generic fold-type (saddle-node) bifurcation can be reduced to one-dimensional dynamics close to the bifurcation becaus…