Multirhythmicity for a Time-Delayed FitzHugh-Nagumo System with Threshold Nonlinearity

Lionel Weicker, Lars Keuninckx, Gaetan Friart, Jan Danckaert, Thomas Erneux

Onderzoeksoutput: Chapterpeer review

2 Citaten (Scopus)

Samenvatting

A time-delayed FitzHugh-Nagumo (FHN) system exhibiting a threshold nonlinearity is studied both experimentally and theoretically. The basic steady state is stable but distinct stable oscillatory regimes may coexist for the same values of parameters (multirhythmicity). They are characterized by periods close to an integer fraction of the delay. From an asymptotic analysis of the FHN equations, we show that the mechanism leading to those oscillations corresponds to a limit-point of limit-cycles. In order to investigate their robustness with respect to noise, we study experimentally an electrical circuit that is modeled mathematically by the same delay differential equations. We obtain quantitative agreements between numerical and experimental bifurcation diagrams for the different coexisting time-periodic regimes.
Originele taal-2English
TitelControl of Self-Organizing Nonlinear Systems
RedacteurenEckehard Schöll, Sabine H.L. Klapp, Philipp Hövel
UitgeverijSpringer International Publishing
Pagina's337-354
Aantal pagina's18
ISBN van elektronische versie978-3-319-28028-8
ISBN van geprinte versie978-3-319-28027-1
DOI's
StatusPublished - 23 jan 2016

Publicatie series

NaamUnderstanding Complex Systems
UitgeverijSpringer
ISSN van geprinte versie1860-0832

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