Wave trains in an excitable FitzHugh-Nagumo model: bistable dispersion relation and formation of isolas

Item Type:	Article
Title:	Wave trains in an excitable FitzHugh-Nagumo model: bistable dispersion relation and formation of isolas
Creators Name:	Roeder, G. and Bordyugov, G. and Engel, H. and Falcke, M.
Abstract:	We investigate the dispersion relations of nonlinear periodic wave trains in excitable systems which describe the dependence of the propagation velocity on the wavelength. Pulse interaction by oscillating pulse tails within a wave train leads to bistable wavelength bands, in which two stable and one unstable wave train coexist for the same wavelength. The essential spectra of the unstable wave trains exhibit a circle of eigenvalues with positive real parts which is detached from the imaginary axis. We describe the destruction of the bistable dispersion curve and the formation of isolas of wave trains in a sequence of transcritical bifurcations unfolding into pairs of saddle-node bifurcations. It turns out that additional dispersion curves of unstable wave trains play an important role in the destruction of the bistable dispersion curve.
Source:	Physical Review E
ISSN:	1539-3755
Publisher:	American Physical Society
Volume:	75
Number:	3 Pt 2
Page Range:	036202
Date:	March 2007
Official Publication:	https://doi.org/10.1103/PhysRevE.75.036202
PubMed:	View item in PubMed

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