What is the theory of catastrophes?

If you ask any schoolboy about his own future, then, as a rule, he will indicate the main milestones: graduation from school, obtaining a diploma of higher or technical education, finding a job, getting married, buying various things (car, apartment), giving birth to children and . In each specific case, the order may change. Asking a middle-aged man about the future, you can hear a similar response, with the only difference being that the reference point will be shifted forward. All this means that we are accustomed to regard the existing order of things as unchanged: every morning in the east the Sun will appear, our houses will not disappear anywhere, there will always be water in the water pipe, heat in the radiators ... We absolutely do not know about that, Which is hidden behind the term "catastrophe theory". But it is completely in vain, because the latest events taking place in the world speak of its importance.

Before we describe what the "catastrophe theory" is, let us recall the formation and development of mathematics in the 18th century. At that time, many scientists were convinced that absolutely all natural and anthropogenic processes can be mathematically described using linear continuous functions. In other words, it was believed that everything reigns in order and there is a direct relationship between the impact and the result, taking into account the intensity (remember the law of conservation of energy). Subsequently, the whole inconsistency of this point of view became clear.

Everything in the world, except for living objects, tends to chaos: things are decrepit and require replacement, the technique breaks down, metal corrodes, etc. This was called entropy. At the same time, there is some organizing force that creates order: atoms are not a random set of particles, but are ordered building blocks, etc. A familiar world exists because of the balance of creative and destructive principles. A small margin is enough to balance the system's balance. After understanding this in the 1970s, a theory of catastrophes appeared, as one of the disciplines in mathematics. One of its virtues is the simplicity of understanding and the ease of proof.

It is worth noting that a catastrophe is a kind of avalanche change of any characteristic of an object, with a minor adjustment of one of its fundamental parameters. There is nothing complicated if you turn to life itself. Let us give an example: the theory of catastrophes asserts that a person sliding on ice is in a stable state. It can be disturbed by a slight external influence: a small stone fell under the feet, the glide suddenly stopped, the center of gravity shifted sharply, which caused a fall. However, after this, according to the theory of catastrophes, there is a new stable state. By the way, the ability to rearrange the leg and maintain the previous position is also taken into account (the sum of the factors).

Of course, since the theory of catastrophes and mathematics are directly interrelated, everything is more complicated than the explanation "on the fingers". Complex formulas are used, a subdivision is performed on a variety of catastrophes. Usually for the explanation in mathematics use the graph of dependences of two parameters. Let's imagine a certain surface, which is (floating) above the coordinate plane. While the surface is smooth or symmetrically folded, we can talk about direct dependence. However, it is necessary to appear a fold, as completely different formulas are used to calculate the peak or catastrophe. If two peaks (folds) are combined, then talk about assembly, etc. A detailed description can be found in the corresponding section of mathematics. This theory is used to model not only natural processes, but also related to the human factor (including the economy).