Abstract:

We discuss some recent progress in the development of a bifurcation theory for random dynamical systems, touching upon the following publications:

1. Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Bifurcation analysis of a stochastically driven limit cycle, Communications in Mathematical Physics 365, 3 (2019), 935-942.
2. Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Conditioned Lyapunov exponents for random dynamical systems, Transactions of the American Mathematical Society 372, 9 (2019), 6343-6370.
3. Thai Son Doan, Maximilian Engel, Jeroen S. W. Lamb, and Martin Rasmussen, Hopf bifurcation with additive noise, Nonlinearity 31, 10 (2018), 4567-4601.
4. Mark Callaway, Thai Son Doan, Jeroen S. W. Lamb, and Martin Rasmussen, The dichotomy spectrum for random dynamical systems and pitchfork bifurcations with additive noise, Annales de l'Institut Henri Poincaré Probabilités et Statistiques 53, 4 (2017), 1548-1574.

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