# Catastrophe Theory

**By**

- A. Okniński, Technical University, Kielce, Poland

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.

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### Book information

- Published: June 1992
- Imprint: ELSEVIER
- ISBN: 978-0-444-98742-6

### Table of Contents

**1. Origin of catastrophe theory.** Philosophy. Mathematics. Experiment. Summary. Evolution of catastrophe theory and its founders. **2. Elementary catastrophe theory.** Introduction. Potential functions of one variable. Functions of two variables. Final remarks. **3. Applications of elementary catastrophe theory (non-chemical systems).** Introduction. Stability of soap films. Thermodynamics and phase transitions. Diffraction catastrophes. The Zeeman model for the heartbeat and the nerve impulse transmission. Population models and sequential models. Relation of the discussed models to chemical systems. **4. Chemical Kinetics.** Introduction. Fundamental concepts of chemical kinetics. Kinetic equations for reactions without diffusion. Kinetic equations for reactions with diffusion. Modelling of the reaction mechanisms by standard kinetic systems. **5. Catastrophes in dynamical systems.** Introduction. Classification. Classification of linear systems. Fundamentals of catastrophe theory of dynamical systems. Classification of catastrophes in dynamical systems. Elementary analysis of dynamical catastrophes. Methods of examination of equations of reactions with diffusion. Analogies between elementary and generalized catastrophe theory. **6. Catastrophes in chemical reactions.** Introduction. The Belousov-Zhabotinskii reaction. Kinetic models and their analysis. Catastrophes associated with the changes in distribution of molecular electron density. Conclusion. Subject Index.