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arXiv · 1512.03002

Uncertainty Transformation via Hopf Bifurcation in Fast-Slow Systems

Christian Kuehn
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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.

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Christian Kuehn. 2015-12-09. Uncertainty Transformation via Hopf Bifurcation in Fast-Slow Systems. https://doi.org/10.1098/rspa.2016.0346

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