Active Media with Long-Range Inhibition

Abstract

In this chapter we consider stationary patterns that are formed in a special class of two-component media, where one of the components can be treated as an activator and the other as an inhibitor. Generally, an isolated element of such a medium can be either bistable, or excitable, or oscillatory. This distinction becomes, however, of minor importance if inhibition is long-range (for instance, when the diffusion constant of an inhibitor component is very large) and if it quickly adjusts to the momentary distribution of an activator. These conditions favor the formation of stable stationary dissipative patterns.