Spatial patterns for reaction-diffusion systems with conditions described by inclusions
A reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions is considered. The main result exhibits a destabilizing effect of these boundary conditions in the following sense. It is proved that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded.
scientific article; zbMATH DE number 1450135
scientific article