Uncertainty Transformation via Hopf Bifurcation in Fast-Slow Systems
arXiv:1512.03002 · doi:10.1098/rspa.2016.0346
Abstract
Propagation of uncertainty in dynamical systems is a significant challenge. Here we focus on random multiscale ordinary differential equation models. In particular, we study Hopf bifurcation in the fast subsystem for random initial conditions. We show that a random initial condition distribution can be transformed during the passage near a delayed/dynamic Hopf bifurcation: (I) to certain classes of symmetric copies, (II) to an almost deterministic output, (III) to a mixture distribution with differing moments, and (IV) to a very restricted class of general distributions. We prove under which conditions the cases (I)-(IV) occur in certain classes vector fields.
19 pages, 5 figure, preprint version; comments and suggestions welcome!