Mathematical and Computer Modeling of the State of Complex Systems under the Influence of Potential Forces

Abstract

This article considers the problem of determining critical points and areas in a system that is exposed to external forces. As a result, the system can lose its stability and go into a non-equilibrium state, and then collapse and cause various kinds of catastrophes. The study of the problem of identification and prediction of disasters is relevant, because allows you to take preventive measures to prevent them and reduce the risks of various negative scenarios. The mathematical theory of catastrophes and methods of the theory of stability find practical applications in various fields of applied mathematics, physics, mechanics, biology, as well as in economics and other sciences. The control of the bifurcation parameters of the system, under which the loss of its stability occurs, makes it possible to maintain its equilibrium state and avoid a catastrophe. As an example, the problem of determining the system deformations that arise under the action of the potential function of classical and couple stresses is given. Analytical and numerical methods for solving this problem and performing calculations using the high-level programming language Fortran, which is widely used for scientific and engineering calculations, contribute to obtaining an adequate result.