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Formation and propagation of localized states in extended systems
Author(s) -
Bestehorn M.,
Grigorieva E.V.
Publication year - 2004
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.200410085
Subject(s) - superposition principle , transient (computer programming) , physics , statistical physics , current (fluid) , complex system , pattern formation , stationary state , current density , classical mechanics , computer science , quantum mechanics , artificial intelligence , biology , thermodynamics , operating system , genetics
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.