Analysis of domain-solutions in reaction-diffusion systems |
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Authors: | L. Schimansky-Geier H. Hempel R. Bartussek Ch. Zülicke |
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Affiliation: | (1) Institut für Physik, Humboldt-Universität zu Berlin, Unter den Linden 6, D-10099 Berlin, Germany;(2) Fachbereich Physik, Universität Augsburg, Memminger Strasse 6, D-86135 Augsburg, Germany;(3) Marine Environment Unit, Joint Research Centre Ispra, I-21020 Ispra (Va), Italy |
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Abstract: | We investigate a standard model for bistable reaction-diffusion-systems, which shares characteristic properties with the van-der-Pol oscillator for distributed generators and the FitzHugh-Nagumo system. In this system we study the effect of a long ranging inhibitor. As a main result we show the existence of two inhomogeneous stationary solutions—the smaller one is always a saddle which corresponds to a critical nucleus, while the larger one arises as astable solution. In carrying out the linear stability analysis for these solutions, we have to treat the Schrödinger-equation for a double-well potential. This is done approximately by a supersymmetric approach which yields the eigenvalues and eigenfunctions of the Schrödinger-equation. Furthermore we compare our analytical findings with numerical results-especially the occurrence of oscillating solutions is shown. |
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