Scenarios of Self-Organization in Real One-Dimensional Systems

Abstract

In real systems there always are small inhomogeneities, and boundary conditions may be other than neutral or cyclic conditions. Because of this, scenarios of self-organization may differ considerably from those discussed in Ch. 21 with reference to ideally homogeneous systems. We would like to emphasize once again that all those effects which are responsible for self-organization (Ch. 20), as a rule, are not linked with fluctuations. In particular, dissipative structures will arise sooner than the critical excitation level A = A c (stratification threshold) is attained (Sect. 9.2) owing to spontaneous formation of an autosoliton near a small inhomogeneity (Sect. 19.4) or near the boundary of the system (Dubitsky — Kemer — Osipov 1987). Small-scale (local) inhomogeneities of size d (lL)½ will modify the pattern of self-organization in not the same way as the large-scale inhomogeneities whose size is d ≫ (lL)½. Now we are going to consider typical scenarios of self-organization in real one-dimensional active systems (Kerner — Osipov 1982b, 1985a, 1990).