B. S. Kerner

Classification of Autosolitons and Phenomena of Self-Organization

In this chapter we consider in brief the connection between the characteristics of active systems and the possible types of autosolitons (Sect. 10.1) and self-organization phenomena (Sect. 10.2) on the basis of our previous discussion and the general theory developed in Part II of the monograph. The results are summarized in Table 3 which offers quick reference as to the classification of systems, the types of autosolitons and other dissipative structures and autowaves, and the effects of self-organization (rearrangement of dissipative structures). For the reader’s convenience, Table 3 also contains references to chapters devoted to this or that particular effect.

Autosolitons in Bistable (Trigger) Systems

Those N and И-systems in which curves LC and ES intersect at three points are usually referred to as trigger systems (Fig. 18.1a). Recall that “local coupling” (LC) and “equation of state” (ES) are functions η(θ) corresponding, respectively, to equations q(θ, η, A) = 0 and Q(θ, η, A) = 0 at a given value of A (Sect. 9.7). In trigger (bistable) systems, two of the three homogeneous states are stable and correspond to the “cold” (θ h 1, η h 1 and “hot” (θ h 3, η h 3) states of the system (Fig. 18.1a). This situation may occur in semiconductors (see, for example, Balkarei – Nikulin 1976, Kerner — Osipov 1985b), in semiconductor structures, as well as in gas plasma and in some chemically reacting systems. Bistable chemical systems are the subject of many reviews, monographs and collected papers, to which we refer the interested reader (see, for example, Zhabotinskii 1974; Field — Burger 1985; Malchow — Schimansky-Geier 1985; Vasil’ev — Romanovskii — Chernayskii — Yakhno 1987; Mikhailov 1990).

Static and Traveling Strata in Solids and Gases

Strata (domains) of electric field occur in various distributed systems. Electrical and thermal domain instability in semiconductors with N-shaped voltage-current characteristic, for instance, has been thoroughly studied both theoretically and experimentally in the 60s and 70s. Especially well known among such instabilities is the Gunn effect, which consists in formation of a static or traveling electric field domain in homogeneous semiconductors with N-shaped voltage-current characteristic (see, for example, Volkov — Kogan 1968; Bonch-Bruevich — Zvyagin — Mironov 1972).

Self-Organization in Two and Three-Dimensional Systems

Self-organization in two and three-dimensional systems depends essentially on the three effects as discussed in Ch. 20: (1) local breakdown in some regions of dissipative structure; (2) activator repumping between fragments of dissipative structure; (3) corrugation of the stratum walls, or corrugation of the walls of a more complicated dissipative structure (Kerner — Osipov 1980, 1985a).

Turbulence in Active Systems

It is the hard regime of excitation of large-amplitude dissipative structures that is realized in the majority of active systems because of stratification of their homogeneous state (Sect. 19.4 and 19.2). As a rule, in real systems a large-amplitude dissipative structure arises spontaneously in the form of one or several autosolitons near the point of stratification of homogeneous state (Sect. 19.4 and 22.1). As demonstrated elsewhere in this monograph, scenarios of self-organization in active systems of diverse nature are essentially determined by the nontrivial properties of autosolitons and interactions between them.

Classification of Active Distributed Media

In this chapter we generalize the results of Ch. 1 – 8, define and explain the main concepts and terms, and offer a classification of active systems (Kerner — Osipov 1983a, 1985a, 1986, 1989a).

“Ball Lightning” in Semiconductors and Gases

In this chapter we consider the effect of formation of highly nonequilibrium steady localized regions (autosolitons) in slightly nonequilibrium stable homogeneous media (Kerner — Osipov 1978, 1985c, 1987). This effect consists essentially in the following.

Structures Near Stratification Point of Homogeneous State of the System

In this chapter we consider such dissipative structures as may arise spontaneously near point of stratification of homogeneous state of the system A = A c . It is emphasized that in real systems autosolitons form spontaneously near point A = A c , (Kerner — Osipov 1985a, 1989a). Spontaneous formation of autosolitons is a result of dynamic rearrangement of the initial almost homogeneous state, and practically is not linked with the presence of fluctuations in the system. Fluctuations may only provoke (with a certain finite probability) spontaneous formation of autosolitons sooner than the critical point is reached.

Static, Traveling and Pulsating Autosolitons

In this chapter we consider certain systems in which it is possible to excite not only traveling but also static autosolitons. Moreover, pulsating autosolitons may arise in such systems, such as change periodically or randomly with the time.

Hot Spots in Semiconductors and Semiconductor Structures

In this chapter we consider autosolitons observed as “hot spots” in semiconductors — that is, local regions of high temperature of semiconductor’s lattice.