The Poincaré map of randomly perturbed periodic motion

DOI10.1007/s00332-013-9170-9zbMath1284.34102arXiv1206.0380OpenAlexW2117475827MaRDI QIDQ379918

Georgi S. Medvedev, Pawel Hitczenko

Publication date: 11 November 2013

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.0380

zbMATH Keywords

limit cycleburstingrandom perturbationsmixed-mode oscillationsfirst return map

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05) Ordinary differential equations and systems with randomness (34F05) Biological rhythms and synchronization (92B25)

Related Items (10)

Stability of the Poincaré maps for a stochastic fast–slow system ⋮ A new model for realistic random perturbations of stochastic oscillators ⋮ Stochastic mixed-mode oscillations in a three-species predator-prey model ⋮ Spectral Theory for Random Poincaré Maps ⋮ Stability and constructions of the Poincaré maps for a class of stochastic partial differential equations ⋮ Stochastic perturbations of periodic orbits with sliding ⋮ Phase-amplitude reduction of transient dynamics far from attractors for limit-cycling systems ⋮ Stability of equilibria of randomly perturbed maps ⋮ From random Poincaré maps to stochastic mixed-mode-oscillation patterns ⋮ The Poincaré maps of a slow-fast stochastic system

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