ABSTRACT
This chapter presents the concepts of attractors, bifurcation, equilibria and stability, fractals, self-organization, and catastrophes. The global picture describes the continuity between highly volatile chaotic processes and simpler ideas of equilibria and stability. Of necessity, this chapter will bear some resemblance to Chapter 2 of Chaos, Catastrophe, and Human Affairs (Guastello, 1995a). One main difference, however, is that some of the more exotic dynamics presented previously have been thrown overboard in favor of the smaller number of simpler dynamics that have found fairly wide applicability in applied psychology. The dynamics of self-organization play a greater role this time around. Hopefully, the range of dynamics in use is a temporary state of affairs arising from this still-early stage of theoretical development and experimental analysis. At the same time, however, the contributions of NDS to substantive theories are not so primitive that they can be dusted off as provocative speculations. Rather, they are growing together in a way that permits a comprehensive social science theory. The presentations that follow emphasize qualitative analysis of phenomena.
I tread lightly on the equations and original mathematical thinking. Fortunately, applied science uses the products of the mathematics; this is not necessary to revisit proofs and such. Several books serve as general references for the sections of attractors, bifurcations, and chaos: R. H. Abraham and C. Shaw (1992) and F. D.
Abraham, R. H. Abraham, and Shaw (1990), Kaplan and Glass (1995), Nicolis and Prigogine (1989), Puu (2000a), and Thompson and H. B. Stewart (1986).
