Hamburg 2001 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 46: Poster
DY 46.37: Poster
Donnerstag, 29. März 2001, 15:45–18:15, Foyer S\ 3
Front Propagation into an Unstable State of Piecewise Linear Reaction-Diffusion System — •Evgueni P. Zemskov1, Vladimir S. Zykov2, Klaus Kassner1, and Stefan C. Müller2 — 1Institut für Theoretische Physik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106 Magdeburg — 2Institut für Experimentelle Physik, Otto-von-Guericke-Universität, Universitätsplatz 2, 39106 Magdeburg
The one-dimensional system considered here consists of two scalar fields: an activator and an inhibitor. The temporal dynamics is described by two differential equations of FitzHugh-Nagumo-type. We approximate a cubic reaction term by linear pieces and consider front propagation from (a) a stable state and (b) an unstable state into an unstable state introducing the traveling frame coordinate. We show that front solution can be derived exactly for a model with equal diffusion constants. The front solutions of the No-dq2+3No-dq-type (two exponential on the negative side is patched together with a sum of three on the positive side of the traveling frame coordinate) were found in the (a)-case and No-dq1+3No-dq-type in the (b)-case. In contrast to the (b)-case, there is no unique solution for the front velocity in the (a)-case. In the (b)-case we derive exact analytical solutions for the velocity equation and for the growth rate of disturbances.