Stable patterns generated by activator-inhibitor systems

The paper is concerned with a discrete morphogenetic model of activator-inhibitor type. The aim is to give a theoretical explanation for what we understand as the first step in pattern formation for a growing object: as long as the object remains small enough, its shape is spatially homogeneous, while passing a critical length results in a spontaneous establishment of a non-homogeneous configuration. We show that, for parameters suitably chosen, there are many stable patterns that can be formed. This fact implies, in particular, a sensitive dependence of the established pattern from the perturbation that causes the object to leave the homogeneous state.