# Analytical And Simulation Models

Model – an object, which in certain circumstances, replace the original, reproducing the interesting properties and characteristics of the original. There are two classes of models: analytical and simulation. The analytical models behavior of a complex system can be written in the form of some functional relations or logical conditions. The most complete study can be carried out in the case when the explicit dependence of linking the unknown values to the parameters of a complex system and the initial conditions of the study. However, this can be done only for relatively simple systems. For complex systems, the researcher has to go to simplify the real phenomena, which makes it possible to describe their behavior and to provide interaction between the components of a complex system.

This allows you to learn at least some general properties of complex systems, for example, to assess the stability of the system, characteristics of reliability, etc. To construct mathematical models provides a powerful mathematical tool mathematical tool availability and the relative speed and ease of obtaining information about the behavior of complex system contributed to the widespread and successful dissemination of analytical models for analyzing the characteristics of complex systems. When the phenomenon in a complex system so complex and varied that the analytical model becomes too crude an approximation to reality, a system analyst is forced to use simulation. In the simulation model the behavior of the components of a complex system described by a set of algorithms who then sell the situations arising in the real system. Modeling algorithms allow you to input data containing information about the initial state of a complex system, and the actual values of system parameters display real phenomena in the system and obtain information about possible behavior of a complex system for this particular situation. It is noted that the predictive capabilities of simulation is much less than analytical models.

The analytical model has several advantages compared to the simulation model. First, the analytical model yields a solution of the problem in complete form. Secondly, the use of analytical model provides a deep analysis. With the help of analytical models can be carried out to study the characteristics of a certain domain of parameters in which the model adequately describes the phenomena or processes. The use of analytical models provides a solution in the form of the functional dependence of the studied characteristics of the model parameters. A simulation model for one cycle of its application calculates characteristics at one point. To obtain the functional dependence of the output characteristic of the model parameters necessary to carry out multiple calculations on the simulation model. On the other hand, to construct an analytical model for complex systems very difficult. With such a construction is required to make important simplifying assumptions that may cause that the model will not adequately describe the process or phenomena. In this sense, the simulations have an advantage because they can be built in the most general assumptions about the system. Consequently, simulation models may be more appropriate. K disadvantage of analytical models is also true that a simple modification of the project or change in the assumptions about the functioning of the structural elements may require a radical restructuring of the model, while simulation models need to change only the input information. Source: Student Portal – StudProspekt. A lot of laboratory work papers.