Spatially inhomogeneous stationary states: dissipative structures

Abstract

Spontaneous breaking of symmetry and the formation of stationary structures in spatially homogeneous systems with local positive feedback, Eqs. (1.1)–(1.3), were first indicated by A. Turing (1952) in his pioneering work on one of the crucial problems in biology of development — morphogenesis. The title of the work we cite was “Chemical foundations of morphogenesis”. After a decade, in the Sixties, such structures have been investigated further by members of I. Prigogine’s Brussels School (Glansdorff and Prigogine, 1971). In their studies the phenomenon was provided with a name, “dissipative structures” (DS), which is relevant to thermodynamical aspects of the problem: the structures exist owing to an influx of energy, substance etc. from the environment and the dissipation within the system. During the past decade, various aspects of the theory of DS and its applications have been investigated in many laboratories (Vasilev, Romanovskii and Yakhno 1979, Kerner and Osipov 1978, 1980, 1983, Belintsev 1983, Mcolis and Prigogine 1977, Romanovskii, Stepa-nova and Chernavskii 1984; Murray 1977).