From random Poincaré maps to stochastic mixed-mode-oscillation patterns
Résumé
We quantify the effect of Gaussian white noise on fast--slow dynamical systems with one fast and two slow variables, which display mixed-mode oscillations owing to the presence of a folded-node singularity. The stochastic system can be described by a continuous-space, discrete-time Markov chain, recording the returns of sample paths to a Poincaré section. We provide estimates on the kernel of this Markov chain, depending on the system parameters and the noise intensity. These results yield predictions on the observed random mixed-mode oscillation patterns. An unexpected result of the analysis is that in certain cases, noise may increase the number of small-amplitude oscillations between consecutive large-amplitude oscillations.
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