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- W3100170025 abstract "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 Poincar'e 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. Our analysis shows that there is an intricate interplay between the number of small-amplitude oscillations and the global return mechanism. In combination with a local saturation phenomenon near the folded node, this interplay can modify the number of small-amplitude oscillations after a large-amplitude oscillation. Finally, sufficient conditions are derived which determine when the noise increases the number of small-amplitude oscillations and when it decreases this number." @default.
- W3100170025 created "2020-11-23" @default.
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- W3100170025 creator A5024817853 @default.
- W3100170025 date "2015-01-08" @default.
- W3100170025 modified "2023-10-15" @default.
- W3100170025 title "From Random Poincaré Maps to Stochastic Mixed-Mode-Oscillation Patterns" @default.
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- W3100170025 doi "https://doi.org/10.1007/s10884-014-9419-5" @default.
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