[PDE&A] Maximilian Engel: Detecting random bifurcations via rigorous enclosures of large deviations rate functions

14 November 2024 16:00 till 17:00 - Location: EEMCS Hall G 36.HB.00.230 | Add to my calendar

We provide a description of transitions from uniform to nonuniform snychronization in diffusions based on large deviation estimates for finite time Lyapunov exponents. These can be characterized in terms of moment Lyapunov exponents which are principal eigenvalues of the generator of the tilted (Feynman-Kac) semigroup.

Using a computer assisted proof, we demonstrate how to determine these eigenvalues and investigate the rate function which is the Legendre-Fenichel transform of the moment Lyapunov function. We apply our results to two case studies: the pitchfork bifurcation and a two-dimensional toy model, also considering the transition to a positive asymptotic Lyapunov exponent.

This is joint work with Alexandra Blessing, Alex Blumenthal and Maxime Breden.