Introduction

In the preceding chapter, a different way of looking at qualitative aspects of studies has been presented, indicating what can happen if the variables and parameters change through some values. In this chapter, we take up another motivation that leads to what are called ‘catastrophes’ dealing again with qualitative aspects of mathematical systems. We begin with the genesis of the ideas as ‘catastrophes’, and then consider the mathematics of it followed by exemplars that become applicable at this stage.

Genesis

Stability continues to be our fundamental concern. The whole universe including biological organisms has some kind of stability as its basis. However, it was the great French mathematician Rene Thom who in his classic book, published in 1975, pioneered the technique of applying a theory of stability to mathematical models of various kinds. This technique naturally did advance the cause of qualitative insight and could also demonstrate that the qualitative understanding of a problem was as adequate as its quantitative understanding. A combination of qualitative information as well as quantitative details tends to make the solution of many problems from diverse areas not only easier but more complete, as well. Sometimes, quantitative methods applied to obtain answers to practical problems such as the structural survival of a certain bridge in high winds, or may be, the continuation of roughly elliptical planetary orbits in the solar system are, in effect, qualitative answers.