If you ask any student about his own future, as a rule, it will indicate the major milestones: graduation, a diploma of higher or technical education, job, marriage, purchase of various things (car, apartment), birthchildren, etc.In each case, the procedure may vary.A middle-aged man asked about the future, you can hear a response like, with the only difference that the starting point will be shifted forward.All of this suggests that we are all accustomed to thinking of the status quo unchanged: every morning in the east the sun will appear, our houses are not going anywhere, in the water will always be water in the radiators - heat ... We did not know about,what lies behind the term "catastrophe theory".And it is in vain, because the latest developments taking place in the world to talk about its importance.
Before describing what "catastrophe theory", recall the formation and development of mathematics in the 18th century.While many scientists were convinced that absolutely all the processes of natural and anthropogenic factors can be mathematically described by a linear continuous functions.In other words, it was thought that in all the kingdom, and the order between exposure and outcome, there is a direct relationship, taking into account intensity (remember the law of conservation of energy).Subsequently, all became clear inadequacy of this view.
Everything in the world, except for live objects, tends to chaos: things deteriorate and need replacement, broken appliances, metal corrodes, and so forth. It was called entropy.At the same time there is some organizing force creates order: atoms are not a random set of particles, and are ordered building "blocks", etc.The familiar world exists because of the balance of constructive and destructive principles.Small enough advantage to balance the system was broken.After realizing that in the 1970s there was a catastrophe theory as one of the disciplines of mathematics.One of its advantages - simplicity and ease of understanding of the evidence.
It is worth noting that the disaster - a kind of avalanche change any characteristics of the object, with a slight adjustment of one of its basic parameters.Nothing complicated, if we look at life itself.Here is an example: catastrophe theory argues that people sliding on the ice, is in a stable condition.It may be a little disturbed by external influence: here under his feet was a small pebble, slip suddenly stopped, the center of gravity has shifted dramatically, which caused the fall.However, after that, according to catastrophe theory, there is a new stable state.By the way, the ability to rearrange the leg and keep the same position also taken into account (the sum of the factors).
course, as catastrophe theory and mathematics directly interconnected, everything is more complicated than an explanation "on his fingers."Uses complex formulas executed subdivision into varieties of disasters.Typically, to explain in mathematics using a graph of dependencies of two parameters.Imagine a kind of surface, located (hovering) over the coordinate plane.As long as the surface is flat or folded symmetrically, we can speak of a direct dependence.However, it should appear crease as applied completely different formula to calculate the peak or disaster.If the two peaks (fold) combined, then talk about the assembly, etc.Detailed description can be found in the relevant section of mathematics.This theory is used to simulate not only the natural processes, but also related to human factors (including economics).
