Dynamics of a stochastic excitable system with slowly adapting feedback
dc.bibliographicCitation.seriesTitle | WIAS Preprints | eng |
dc.bibliographicCitation.volume | 2678 | |
dc.contributor.author | Franović, Igor | |
dc.contributor.author | Yanchuk, Serhiy | |
dc.contributor.author | Eydam, Sebastian | |
dc.contributor.author | Bačić, Iva | |
dc.contributor.author | Wolfrum, Matthias | |
dc.date.accessioned | 2022-06-30T12:42:33Z | |
dc.date.available | 2022-06-30T12:42:33Z | |
dc.date.issued | 2020 | |
dc.description.abstract | We study an excitable active rotator with slowly adapting nonlinear feedback and noise. Depending on the adaptation and the noise level, this system may display noise-induced spiking, noise-perturbed oscillations, or stochastic busting. We show how the system exhibits transitions between these dynamical regimes, as well as how one can enhance or suppress the coherence resonance, or effectively control the features of the stochastic bursting. The setup can be considered as a paradigmatic model for a neuron with a slow recovery variable or, more generally, as an excitable system under the influence of a nonlinear control mechanism. We employ a multiple timescale approach that combines the classical adiabatic elimination with averaging of rapid oscillations and stochastic averaging of noise-induced fluctuations by a corresponding stationary Fokker-Planck equation. This allows us to perform a numerical bifurcation analysis of a reduced slow system and to determine the parameter regions associated with different types of dynamics. In particular, we demonstrate the existence of a region of bistability, where the noise-induced switching between a stationary and an oscillatory regime gives rise to stochastic bursting. | eng |
dc.description.version | publishedVersion | eng |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/9328 | |
dc.identifier.uri | https://doi.org/10.34657/8366 | |
dc.language.iso | eng | |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | |
dc.relation.doi | https://doi.org/10.20347/WIAS.PREPRINT.2678 | |
dc.relation.hasversion | https://doi.org/10.1063/1.5145176 | |
dc.relation.issn | 2198-5855 | |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject.ddc | 510 | |
dc.subject.other | Excitability | eng |
dc.subject.other | adaption | eng |
dc.subject.other | coherence resonance | eng |
dc.title | Dynamics of a stochastic excitable system with slowly adapting feedback | eng |
dc.type | Report | eng |
dc.type | Text | eng |
dcterms.extent | 19 S. | |
tib.accessRights | openAccess | |
wgl.contributor | WIAS | |
wgl.subject | Mathematik | |
wgl.type | Report / Forschungsbericht / Arbeitspapier |
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