Relation of the discussed models to chemical systems

In Section 1.3 we described the systems in which qualitative and discontinuous changes of state, that is catastrophes, could be observed at a continuous variation in control parameters. The catastrophes occurring in some systems were discussed in terms of elementary catastrophe theory in Sections 3.2-3.6. The discussion was confined to non-chemical systems such a classification (as we shall see later) being rather artificial. Catastrophes (static and dynamic) occurring in chemical systems will be described in Chapters 5, 6. 

Many of the considered problems, such as the problem of stability of soap films, the liquid-vapour phase transition, the diffraction phenomena, descriptions of the heartbeat or the nerve impulse transmission, catastrophes described by non-linear recurrent equations have a close relation to chemical problems. 

The stability of thin films and the catastrophes of film systems may play a crucial role in the case of chemical reactions proceeding at the boundary of a liquid phase and another phase. Phase transitions are of a great significance in physical chemistry. The diffraction phenomena for the 

Schrodinger equation and the corresponding diffraction catastrophes occurring at collisions of molecules are important from the viewpoint of the description of chemical reactions taking place upon contact (collision) of molecules. As shown in Section 1.3, recurrent equations appear from a description of the kinetics of chemical reactions. 

The method used by Zeeman to model the heartbeat and the process of nerve impulse transmission by means of differential equations (see Section 3.5) is frequently employed in chemical kinetics (where it is called the Tikhonov method or the method of stationary concentrations). Application of the method to chemical kinetics equations will be discussed in Chapter 4. 

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