At the end of XX century global threats and risks have become the source of many emergency situations. Planning of the efficient answer, choice of the optimal strategy requires developing of an interdisciplinary approach, which can be called the mathematical theory of risk and safety. This approach is based upon computer modelling and the concepts of synergetics (nonlinear dynamics) and the results of other natural and social sciences. The successes of the recently appeared theory of self-organized criticality can be considered as an evidence in favour of this approach. Within the frames of this theory it became possible to find out the universal characteristics which are common for such phenomena as earthquakes and stock exchange crisises, snow avalanches and leaks of confidential information. The power-low probability distributions are characteristic of all of them, which makes one to take into account rare catastrophic events, since they essentially contribute to the averages. Another example is the theory of channels and jokers, which proposes an alternative approach for the description of a number of emergency situations, cognitive processes, to the description of predicting computer systems. Some other recently appeared ideas in this field are also discussed in this paper.

Mathematical modelling in actual problems of science and technics

Malinetskii Georgii Gennadyevich,  ,  orcid.org/0000-0001-6041-1926,  KIAM RAS