1.2. Classification of models

The problem of classification models, as well as any sufficiently complex phenomena, processes, systems, complex, multifaceted and difficult to solve. The objective reason is that researchers are interested only in a single property system (object, process, phenomenon), which is to display and a model. Therefore, the basis for classification can put a variety of different features: a way of describing, functionality, degree of detail, structural properties, application, etc.

Consider some classes of models.

1. By purpose models are distinguished:

• research (trained, cognitive), intended to generate knowledge by studying the properties of the object;

• Training for transmitting knowledge about the object being studied;

• Working (pragmatic) designed to generate the correct action in pursuit of the goal.

To research models are semi-natural stands, physical models, mathematical models. Note that the research model can act as training, if they are intended to transfer knowledge about the properties of the object. Examples of working models are: the robot; autopilot; mathematical model of an object embedded in the control system or control; artificial heart, etc. At the same time, research and training model to approach the reality, and working models must reflect this reality. Clear distinction between these models does not exist. For example, a research model that adequately reflects the properties of the object can be used as a work. Research models are carriers of new knowledge, training models combine old knowledge with new. Working models idealize the accumulated knowledge in the form of ideal action for the implementation of certain functions that it would be desirable to implement.

2. Upon reflection modes of the system are distinguished:

• Static models that reflect the steady (equilibrium) modes of operation of the system;

• Dynamic that reflects unsteadies (non-equilibrium, transient) modes of operation of the system.

Static modes elements, objects, systems reflected in their static characteristics (linear, nonlinear) and describes the relevant algebraic functional dependencies.

3. According to the method of creation (construction) models are distinguished:

•abstract (deductive, speculative, ideal) model built by means of thinking based on our consciousness;

• Material (physical, real) models constructed by means of the material world to reflect its objects, processes, etc.

Abstract models - are ideal design in our minds in the form of images or representations of various physical phenomena, processes, situations, objects, systems. Examples of abstract models can serve any hypothesis about the properties of matter, the assumptions about the behavior of complex systems under uncertainty, or a new theory of the structure of complex systems. On abstract models and speculative analogy (similarity) between the model and the original M S is constructed ideal (deductive) modeling. There are two types of ideal modeling: formalized and non-formalized (intuitive). To formalize the abstract models are symbolic models, including mathematical and language constructs (programming languages ​​, natural languages ​​), together with the rules of their transformation and interpretation. An example of symbolic models can serve as blueprints, plans, diagrams, formulas, etc. Mathematical modeling - a special case of the landmark modeling. Here conversion formulas are based on the rules of logic and mathematics.

Mathematical model - an object that has the following prototype to -one correspondence: 1) structure, i.e. composition of elements and relationships between them; 2) the equations describing the properties of these elements and their relationships. In this mathematical model of a complex system can be treated as a set of mathematical models of elements, interconnected and interacting with each other and adequately reflect the synergistic properties of the system.

When we are figurative modeling models are constructed from any visual elements (elastic spheres, the fluid flows, the trajectory of motion of bodies, etc.). The analysis is carried out mentally shaped models and can be attributed to the formalized modeling when the rules of engagement images clearly formalized. This type of simulation is used in a thought experiment.

This thesis project is an attempt to introduce social scientists with the mathematical formalism and the modern methods of solving sociological problems. Here is a partial list of such problems:

• Data processing and analysis of surveys and other sociological studies

• The construction of mathematical models of social processes and phenomena

• Explanation and prediction of social phenomena

Mathematical modeling is to replace the real object of his mathematical model, followed by the study of the latter. Kind of mathematical model depends on the nature of the real object, and the object of research problems and the required reliability and accuracy of the solution of this problem.

Multidimensional scaling - mathematical tools for processing the data on the relationship between the investigated objects to represent these objects as points of a space perception. This method allows to detect and interpret the latent (i.e., hidden and not directly observable) signs explaining the links between objects under investigation . The manual as a method of multidimensional scaling method considered metric Torgerson .

Another object of processing is to reduce the dimensionality of the data, losing the least amount of information. This allows the first to get rid of "noise», i.e. part of the data that contains no useful information and error and error. Secondly, the smaller dimension of the data, the easier they are to further study and interpretation. As device dimensions decrease the data in the manual describes the method of principal components.

All processes developing in time and having a causal relationship is modeled by differential equations (in the case when the system is described by a single characteristic) and systems of differential equations (such as the characteristics of a few). As an example, the simulation of such processes in the manual gives some examples of growth of the population of a closed ecosystem.