Formation and propagation of localized states in extended systems

We study a one‐species‐diffusion equation supplemented by a nonlinear saturation term. If this term includes temporal delay, a rich spatio‐temporal behavior already at the critical point where the steady homogeneous solution gets unstable is expected. Normal form transformation into a complex Ginzbu...

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Bibliographic Details
Published in:Annalen der Physik 2004-07, Vol.13 (7-8), p.423-431
Main Authors: Bestehorn, M., Grigorieva, E.V.
Format: Article
Language:English
Subjects:
delayed systems
excitable media
Pattern formation
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Summary:We study a one‐species‐diffusion equation supplemented by a nonlinear saturation term. If this term includes temporal delay, a rich spatio‐temporal behavior already at the critical point where the steady homogeneous solution gets unstable is expected. Normal form transformation into a complex Ginzburg‐Landau equation shows that the condition for phase turbulence is always fulfilled. As a secondary instability of these chaotic states well ordered spiral waves and targets are found numerically. Here the system shows features well‐known from excitable media. Finally we propose the construction of logical circuits by means of a network built up by one‐dimensional excitable media.
ISSN:0003-3804
1521-3889
DOI:10.1002/andp.200410085