ANALYSIS OF DOMAIN-SOLUTIONS IN REACTION-DIFFUSION SYSTEMS

We investigate a standard model for bistable reaction-diffusion-system s, which shares characteristic properties with the van-der-Pol oscilla tor for distributed generators and the FitzHugh-Nagumo system. In this system we study the effect of a long ranging inhibitor. As a main res ult we show the existence of two inhomogeneous stationary solutions - the smaller one is always a saddle which corresponds to a critical nuc leus, while the larger one arises as a stable solution. In carrying ou t the linear stability analysis for these solutions, we have to treat the Schrodinger-equation for a double-well potential. This is done app roximately by a supersymmetric approach which yields the eigenvalues a nd eigenfunctions of the Schrodinger-equation. Furthermore we compare our analytical findings with numerical results - especially the occurr ence of oscillating solutions is shown.