This chapter discusses the origin of catastrophe theory. Catastrophe theory deals with the nonlinear phenomena in which a continuous change in control parameters results in a discontinuous alteration of a quantity characterizing the examined system. It is well suited for the investigation of the nonlinear equations of chemical kinetics, describing chemical reactions. Chemical reactions without diffusion are classified from the standpoint of catastrophe theory, and the theoretical results for the reactions with diffusion are presented. The connections among the various domains of physics and chemistry dealing with nonlinear phenomena and the progress achieved in catastrophe theory are discussed. The theory describes only such phenomena whose form is resistant to perturbations–– that is, structurally stable. Catastrophe theory describes changes in the form taking place as a result of continuous variations of control parameters, emphasizing qualitative, structurally stable changes in the form. The most important notions of elementary catastrophe theory, such as structural stability, sensitive state, codimension, universal unfolding, have formed the basis for generalizations going beyond gradient systems.
From Noah's flood to the Haitian earthquake, from the Black Death to the Great War, catastrophes have threatened, disrupted, and overturned patterns of daily existence. As radically disordering events, catastrophes have the power to lay bare the fragility of social and institutional architectures and to make painfully clear the weaknesses and vulnerabilities in the organization of social life. At the same time, by disrupting the fundamental mechanisms and infrastructures of social order, catastrophes serve to define the conditions that inform our sense of the normal. While much attention has been devoted to the study of specific catastrophic events, surprisingly little academic attention has been directed to the concept of catastrophe itself. This course sets out to study the social, cultural, and historical meaning of catastrophe. We will examine the role and representation of catastrophe in religion, the visual arts, literature, law, and politics. At a time when societies are directing an unprecedented level of resources and ingenuity to anticipating and mitigating catastrophic events, we hope to better appreciate catastrophe as a key ordering term of civilization--as the specter of disorder that continues to haunt our social and political imagination.