Approaches to the Development of Complex Systems Models

The paper discusses the problem of mathematical formalization and creation of models of complex systems. It is noted that depending on the availability of information on the properties of the system, various approaches to the development of its models are possible including the systematization of problem statements in terms of a priori information about the object. Features of the development and possibilities of using mathematical models in the conditions of detailed, partial and missing a priori information about the properties of the system are described. Special attention is paid to the problem of creating adequate models of complex systems under uncertainty. Examples of such systems are natural systems, modern industrial enterprises, socio-economic systems. Perspectivity of the cybernetic principle of the “black box” is indicated, when the structure of the model is set by a certain universal mathematical model without reference to the structure of a real object, and the parameters are determined knowing the reaction to known input effects. From the user's point of view, the model structure hidden in the “black box” imitates the behavioral features of a complex system. Such models are called information models. Classes of problems of reconstruction of model equations of complex systems are formed. Examples of solving problems (in the study of real complex processes) based on information models are given. It is noted that the key point in the development of the information model is to check its suitability for the solution of the practical problem associated with the assessment of adequacy in relation to the properties of the object of interest. Examples of different types of adequacy areas are given and also their features are given.