Uncertainty transformation via Hopf bifurcation in fastslow systems
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.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 April 2017
 DOI:
 10.1098/rspa.2016.0346
 arXiv:
 arXiv:1512.03002
 Bibcode:
 2017RSPSA.47360346K
 Keywords:

 Mathematics  Dynamical Systems;
 Mathematics  Classical Analysis and ODEs;
 Mathematics  Probability;
 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 19 pages, 5 figure, preprint version