Uncertainty transformation via Hopf bifurcation in fast-slow systems

Christian Kuehn

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


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.

Original languageEnglish
Article number20160346
JournalProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Issue number2200
StatePublished - 1 Apr 2017
Externally publishedYes


  • Fast-slow systems
  • Hopf bifurcation
  • Random initial condition
  • Uncertainty propagation


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