ABSTRACT
The dynamics of spatially distributed nonlinear systems is characterized by a set of features, of which the self-organization phenomenon is one. This means that, as a result of the nonlinear interaction in a system, some typical inhomogeneous structures can form, and they often derive the asymptotical behavior of solutions by arbitrary initial conditions. Such structures characterize specific properties of a given nonlinear medium and are currently the object of intensive study in the natural sciences. One of the possibilities of a nonlinear system asymptotical evolution, which is often observed, is the formation of nonstationary, for instance, autowave structures; a corresponding example was considered in the previous chapter. Another is the asymptotical formation of stationary dissipative structures corresponding to the local minima of energy functional in the system.1
