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Catastrophe Theory was introduced in the 1960s by the renowned Fields Medal mathematician René Thom as a part of the general theory of local singularities. Since then it has found applications across many areas, including biology, economics, and chemical kinetics. By investigating the phenomena of bifurcation and chaos, Catastrophe Theory proved to
This advanced-level treatment describes the mathematics of catastrophe theory and its applications to problems in mathematics, physics, chemistry and engineering. 28 tables. 397 black-and-white illustrations. 1981 edition.
An introduction to catastrophe theory, a mathematical theory which deals with those changes which occur abruptly rather than smoothly. Includes many applications to illustrate the different ways in which catastrophe can be used in life, physical and social sciences.
From Catastrophe to Chaos: A General Theory of Economic Discontinuities presents and unusual perspective on economics and economic analysis. Current economic theory largely depends upon assuming that the world is fundamentally continuous. However, an increasing amount of economic research has been done using approaches that allow for discontinuities such as catastrophe theory, chaos theory, synergetics, and fractal geometry. The spread of such approaches across a variety of disciplines of thought has constituted a virtual intellectual revolution in recent years. This book reviews the applications of these approaches in various subdisciplines of economics and draws upon past economic thinkers to develop an integrated view of economics as a whole from the perspective of inherent discontinuity.
René Thom, the famous French mathematician and founder of catastrophe theory, considered linguistics an exemplary field for the application of his general morphology. It is surprising that physicists, chemists, biologists, psychologists and sociologists are all engaged in the field of catastrophe theory, but that there has been almost no echo from linguistics. Meanwhile linguistics has evolved in the direction of René Thom’s intuitions about an integrated science of language and it has become a necessary task to review, update and elaborate the proposals made by Thom and to embed them in the framework of modern semantic theory.
This book aims to provide a straightforward introduction to chemical applications of the catastrophe theory. It is primarily intended for chemists interested in placing chemical reactions in the broader context of non-linear science, but it has a practical relevance for scientists in general. Catastrophe theory deals with those non-linear phenomena in which a continuous change in the control parameters results in a discontinuous alteration of a characteristic quantity of the system. The author discusses the origins of catastrophe theory, giving examples of occurrences in the areas of physics, chemistry and biology. Elementary theory and non-chemical applications are also described. The chemical kinetics and methods of analysis of chemical kinetic equations arising from elementary and generalized catastrophe theories are reviewed. Finally, the theory is applied to analyse and classify phenomena associated with the stability loss that may occur in chemical reactions. The book contains over 100 figures and an extensive subject index.
Michel Henry uses the fall of communist regimes to reflect on the place of the individual in the late capitalist moment.