| Abstract: |
| In many situations, deterministic dynamical systems may exhibit non-trivial attractors which collapse to a random point under the addition of Gaussian noise. This phenomenon is widely known as synchronization by noise and seems to make bifurcations of attractors to higher-dimensional objects disappear in the stochastic case.
This point of view was first challenged by Callaway et al. 2017 with respect to the pitchfork bifurcation in the presence of additive noise, showing a transition from uniform to non-uniform snychronization mirroring the original bifurcation.
In this talk, I will give a summary on results from co-authors and myself that have extended these observations to multiple and infinite dimensions and have provided a quantitative analysis via large deviation estimates for finite-time Lyapunov exponents. I will also mention current efforts to fully transfer this framework to SPDEs. |
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