content

introduction

1. Chapter 1. Analytical part .

 General theory of modeling

1.1. Modeling as a method for studying complex systems

1.2. classification of models

1.3. Main stages of mathematical modeling

1.4. Mathematical Modeling and computerization or simulation models

2 . Chapter 2. Practical part. Modeling family

2.1 Background of the model family

2.1.1 The model of adaptive behavior of the family. Formalization of the family

2.1.2 Model Implementation

2.1.3 The computer experiment

2.2 Model " predator-prey "

2.3 Model " Family History "

2.4 Investigation of the stability of the mathematical model

2.5 Model " Trade union activities "

3. Chapter 3 part 3. Economical part

4 . Chapter 4.Obzh

conclusion

References

Introduction

Illustrate and confirm the research contained in this thesis work, is an article by the famous American sociologist Robert Makginns "New methods of research." The article appeared in 1968 in the famous collection «American Sociology: Perspectives, Problems, Methods», edited by T. Parsons. McGinnis warned of impending revolution sociology regarding the mathematical sciences; radical future events that will soon bring as great achievements? And serious losses.

He wrote: «Despite the lack of mathematics might even say an aversion to it - in traditional graduate programs, some sociologists begin to open up for her as a potential for each other language theory. They are attracted by the hope, perhaps even the promise, which promises on improving math sociological theory ...»

Evidence of the revolution in the methods is to R.Makginnis not only appeal to the language of mathematics, but also the use of computers. Copyright (like many of his contemporaries) writes that the computer in sociology is not only ultra-fast calculating machine.

In the classic work of Jean -Francois Lyotard's «postmodern condition " informatization of society associated with the emergence of special postmodern vision of the world. French philosopher notes that «with this change in the nature of general knowledge cannot remain unchanged." Dissemination of information technology inevitably changes the status and nature of scientific knowledge. What is expressed in this change?

The answer is simple, changes are expressed in imitation of reality, namely, in imitation of society.

Characteristic of modern science is that the material is increasingly being replaced experiment experimental models. "If earlier theories could only be built on the basis of some order inherent things , it is now quite possible without access to the simulation of any real referents , such as computer simulations of natural , technological and social processes."

Modern researcher immersed in virtual reality simulations, building artificial society artificial people. Borrowing scheme to determine the universal properties of virtual reality; consider the idea of computer simulation.

Undoubtedly, computer simulation is one cyber prosthetics real society. The real author of the model of society, to his prosthesis "artificial society. " The researchers have to limit the variety of options, discarding some features and simplifying others.

Computer simulation - a typical area of ​​knowledge, which has a specific «postmodern sensibility» - a special, pluralistic attitude to the world, to avoid excessive generalization and dictate totalitarization truths. Generated postmodern information society, it also suggests a lack of invariant basic truths for different classes of objects. This type of modeling «opens" a variety of sociological theories. Using realistic theoretical schemes and models, the researcher is immersed in an exciting and fruitful work.

At the same time, modeling society, computers are a unique tool for generating theory. It is known that computer experiments are very promising for the development of sociological theories, through which you can compile large tracts of available data and with greater unity of purpose to organize the process of empirical research.

However, as with any method that computer simulation is quite controversial ideas and illusions. We shall not discuss here the arguments held opponents of quantitative methods in sociology regarding mathematics. The essence of the trap, into which the sociologists, using computer modeling, lies in the nature of mathematical language. As he wrote the famous Robert McGinnis: "Mathematics - a language that is rich, but not ambiguous, stingy, but not dogmatic. Modern spoken language, even liberally laced with sociological jargon, suffers in this regard (i.e., as an instrument of theory) serious flaws. "

For several years, with the development of computer technology the opportunity to solve engineering geometrical problems by numerical simulation. In memory of the computer created on the basis of digital geometric objects and geometric relations , adequate real and reduced to the numerical solution of the handling of information , or , as they say, mathematical models.

Of the present stage of technological development is a new approach to the design and development of new products based on the principle of optimization parameters of the product at the preliminary design stage . Depth and comprehensive analysis of the decisions taken at the design stage can significantly reduce the time and cost of testing , debugging and implementation of products into production . Shortening the development of new models and the acceleration of scientific and technological progress is impossible without the wide introduction of computer technology in the design process .

From the perspective of the sociology of modeling - an effective means of knowledge of nature. Process modeling assumes:

- The research object;

- The researcher to whom a specific task;

- Model created to obtain information about the object and necessary to solve the problem.

Computer experiment - the transition from study to study the real object of its mathematical model.

Advantages of computational experiment are:

- The possibility of studying the object without modification of the facility or system;

- The possibility of studying each factor separately, then while in reality they operate simultaneously;

- The ability to study unrealizable in practice processes.

Computational experiment involves the following steps:

- A physical description of the process, i.e. clarification of laws leaked phenomena.

- Development of a mathematical model.

- Algorithm or method for solving equations.

- Development of programs.

- Settlement, results analysis and optimization.

This thesis project was written taking into account all the above theories and statements. The urgent socio -psychological problems of society.

Objective: to consider a number of social and psychological problems of society, and to build a specific computer model to make predictions, to identify the current status of the problem.

Research objectives:

1. Identify the most pressing social problems.

2. Construct a mathematical model of each of the problems.

3. Based on the mathematical model of computer modeling done (write code) , allowing to identify certain graphs, charts .

4. Based on the identified charts and graphs make certain projections and analyzes

Object of study is the relationship existing on the example of one family; crisis situation in union activities

The subject of research is mathematical and computer modeling of trade union activities of one firm, mathematical modeling and the development of respect in the same family

Chapter 1. Analytical part.

General theory of modeling

By modeling broadly understand not only the process of building , learning and improvement models, but their use in scientific research, including experimental , as well as their application directly in the planning , management,

predicting, monitoring, etc.

 Modeling as a research method is a powerful tool of knowledge throughout the history of mankind. One example of a man-made system of models that adequately reflects the wide range of phenomena and processes of the real world, are models of classical mechanics.

Modeling as a tool for learning requires creativity and a certain art of handling them. On the other hand, modeling as a science is based on the scientific knowledge of the area where the tool is used knowledge. For example, to construct a mathematical model of the aircraft (LA) requires knowledge of the laws of aerodynamics, mechanics, aircraft movement in the air and airless environment. Only professional knowledge researchers combined with a creative approach to the problem at hand can be the basis for the successful application of the modeling method. Modeling process itself involves a way of studying the object in which the model, in terms of research objectives, quite accurately (adequately) and adequately replaces the object under study.

There are quite a number of definitions of «model." Some of them are too abstract, others - too specific. They all reflect one or another side of this multifaceted concept.

Model - an auxiliary entity (a device agent) which may be replaced by another object.

Model - a simplified representation of another object or process.

Model - a form of representation and the existence of our knowledge.

Model - a tool for learning about the world.

In what follows we adopt the following definition of the model, which is ; is narrower and more specific.

Definition 1. Object M is defined in terms of the system model (object, process conditions, situations) S With respect to a plurality of its characteristics (properties, features) if M is constructed to simulate the characteristics of these S.