Model-is the system, the study of which is the means of obtaining information about the other system. The need for the model similarity with the object of research is reflected in the definition of V. Mogilev, «a model is called specifically for the convenience of researchers synthesized the object that has the necessary degree of similarity to the original». [1]

The research focus is logical model involves the presentation to it the following requirements:

— The adequacy or the ability of the model to reproduce the problem which is interested by the researcher;

— Accuracy, proximity to the observation data of the object of study; — Universality, applicability of the model to a number of similar objects;

— Economy, quality, comparability model, which integrates the adequacy of performance, accuracy and flexibility, and the cost of construction and study models. Successful model should be recognized, in which a compromise is reached between the results of research and the costs of their implementation.

It says about, T. Naylor, indicating that the quality of the model is determined by how successfully, in accordance with the purpose of research, it combines two contradictory beginning — simplicity and realism. [2] On the one hand, the model must be realistic, reflect most important quality of an object, and on the other hand, it should be quite simple, inexpensive, easy to use, and including in practice.

The research potential of the model is not limited to the ability to monitor the behavior problems, models are developed and used to understand the impact of decisions on the interest of the researcher or the reality of the problem.

Features modeling are secured him for several centuries a prominent place in the methodology of social sciences. Noting the systematic knowledge, continuity of sociology to abstract science, Auguste Comte joined the social sciences in the framework of social physics [3]. So natural sciences to the exact classification of Comte is public knowledge on social statics and social dynamics!

The global economic crisis at the beginning of the last century, science has drawn attention to the problem of macroeconomic equilibrium. In the works of George. Keynes, R. Solow, P. Samuelson, to a large extent determine the level of analysis in economic science, the focus is shifting towards issues related to the study of macroeconomics at the equilibrium point or its vicinity. Development within the framework of the concept of equilibrium is a sequence of equilibrium states, alternating short duration transients. Perhaps the greatest extent this view of the development of dynamic processes corresponds to the well-known saying of Leibniz that «nature does not make leaps.»

Accordingly, in the mathematical formalism of research dominated equilibrium models based on the assumption of a linear evolution operator of the system, the smoothness of the approximating functions. Such behavior of the variables allows the use of the machine differential, integral calculus, analytical determination of the trajectories of economic development.

The growth of the scale of social production on the background of the increasing relevance of environmental issues, inter-ethnic, inter-confessional contradictions, became the starting point of transition to a new state of the world. Regional problems cease to be local and take on global importance, as countries, regions, people become part of a single socio-economic system in which the elements, their behavior is closely interconnected and interdependent.

Along with the benefits of globalization, which are expressed in the possibility of access to international, inter-regional markets for goods and factors of production, improvement of technologies, regions are facing new challenges, the outflow of capital, labor, worsening demographic, environmental issues, which together determine the existence of a set of imbalances of regional economy , the nonequilibrium nature of its development, as well as a sharp contradiction between the content of scientific problems and opportunities of the mathematical apparatus.

Awareness of the non-equilibrium nature of the dynamics of socio-economic systems, their openness, and, consequently, depending on the state of macro, stimulated interest in the problem of stability of regional development trajectories with respect to perturbations of the environment, change the operation mode. More aggressively, in theoretical and methodological basis of the study of social and economic systems, along with the equilibrium models take place and such a relatively new field of knowledge, as a synergist, bifurcation theory, catastrophe theory, system dynamics

Synergetics — an interdisciplinary field of science that studies the general laws of phenomena and processes in complex non-equilibrium systems based on the inherent principles of self-organization [1]. The scientific revolution brought term physiologist Sherrington in the study of muscular systems and management on the part of the spinal cord. Later, the term was used by G. Haken, the study of the laws of self-organization of complex systems [3]. It turned out that the principles of self-complex systems are the same, whatever the nature of the system, and therefore may be represented by the general mathematical technique for them. The following provisions can be considered the most significant findings of qualitative studies of complex systems:

1. The non-equilibrium systems are essential attributes of its development. From the standpoint of synergy, the development system is a sequence of its states near some equilibrium level, with subsequent transition to a new level of development, characterized by the renewed structure. To go to a new level, the system has become unstable.

 2. Only a fairly sophisticated system capable of evolution. The number, diversity of connections between elements of the system are determined by its ability to self-organize. It is not enough complex systems under the influence of external forces are destroyed.

 3. A key ingredient of self-organization mechanism — random deviations in the behavior of elements of the system (fluctuations). It turns out that random fluctuations of system elements can combine to define system behavior. Moreover, the further the system from the equilibrium state, the more clearly the corporate behavior of its elements. If stable, adaptive systems such deviations shall be canceled by negative feedback, evolving systems, they accumulate, and with sufficient energy from the outside, are able to undermine the system, and after a short chaotic state result in a new order.

4. Developing the system should be open, allowing you to receive energy from the environment necessary for self-organization and ordering. Closed system, according to the second law of thermodynamics, comes to a state of maximum entropy and evolution ceases.

5. The establishment of a stable system operation mode is associated with the passage of the bifurcation points, or conditions characterized by a high degree of uncertainty of the choice of the way.

One of the pressing problems of the analysis of the dynamics of socio-economic systems is to assess the sensitivity to a change in the parameter values. The theoretical basis of this analysis is the position of bifurcation theory. The basic ideas of the theory go back to the works of Poincare and AM Lyapunov. Word bifurcation means «split» and is used as a symbol hopping, happening with a smooth change of the parameter values ​​in the system [2]. Bifurcation theory studies the change of the qualitative picture of the partition of the phase space of the system when changing the values ​​of its parameters. With regard to the social and economic systems of the study of the phase space is of considerable interest because decisions need to take into account different scenarios of environmental conditions, the variation of the control modes, and, consequently, the system reacts to such changes. From a position of bifurcation theory, a good system should be recognized that in which it is possible to reach a compromise between roughness and sensitivity reactivity of the system. Rough system — it is such a qualitative nature which the movements do not change for a sufficiently small change in the parameters [1]. Rudeness preserves the character of a slight change in environmental conditions, while the sensitivity distinguishes a system capable of responding promptly to the control commands.

Bodies of regional management are widely used simulation capabilities in the form of charts, graphs, equations, when planning production activities, the distribution of budget funds, the formulation of regulations of interaction between authorities and others. At the strategic management level of mental simulation is applied, harping situations, usually within narrow context. Perhaps the common features used analysis tools are focus on the static properties of the object, the short-term horizon of the study, the limitations of the problem that is incompatible with the system, the dynamic nature of contemporary problems of science.

 It is becoming apparent contradiction between analytical, predictive capabilities of the regional administration and the maintenance of regional problems. The sharpness of the contradiction depends on several factors that are objective or subjective.

The natural limitation of the scope of the simulation is either a mismatch of existing models of disequilibrium noted above, the non-linear nature of the development, or their excessive theorizing, excluding obtain reliable results that are of practical importance. In this regard, they do not remember the words of Wassily Leontief, that the growth of distrust in the analysis of the results obtained on the basis of the models is the «neglect of academic economics stubborn, empirical, systematic analysis and passion elegant, but empty, formal, mainly mathematics, theoretical exercises. » The situation is compounded by the fact that the verification of the adequacy of the models is often formality, and as a result, a large number of works are in the field of mathematical modeling of regional systems, and exceptional examples of the use of research results in the daily activities of government.

These conflicts cause the need to improve the methodology of the study of regional processes. Among the areas of this improvement, the most promising are:

1. Consideration of the region as a complex, evolving system, the behavior of which is formed by the interaction of its elements, the system and the external environment. At the same time, the nature of the evolution of socio-economic processes, formed back Information links. Positive feedbacks initiate and develop changes in the system and the negative feedback ensure its stability.

 2. Organization of the study from the perspective of an interdisciplinary approach. The dominant point of view of adequacy for modeling socio-economic processes of a certain level of mathematical training, is transformed into a collective idea of ​​the necessity of research, uniting the efforts of specialists in different fields of knowledge, areas of production and management. Experience in modeling complex systems strongly indicates the possibility and necessity of integration of knowledge in the field of psychology, management, organizational development.

3. Creating a model adequately complex, non-linear nature of the socio-economic processes, based on the increasing computing capacity, provide a solution problems of analysis, forecasting regional development. It appears that this task will contribute much practical orientation of research and scientific development of high quality estimate may be used in their daily work of regional management bodies.

Among the reasons hindering the practical realization of the growing modeling features include subjective factors: steady linear way of thinking, a focus on short-term objectives that ignore the proportions of regional reproduction cycles and trends of the environment.

It seems that the policy of a gradual increase in the level of requirements for regional management, increased competition in the inter-regional markets for goods and factors of production will contribute to the focus on a deep, systematic analysis of regional processes, and on this basis the development of the mental model of regional governance.

Critical analysis of the application of instruments of science capacity, relatively complex, dynamic regional development problems enables us to justify the conclusion about the need to improve the methodological support research on socio-economic processes from the perspective of a systematic approach, based on the joint efforts of scientists, experts in the field of public administration, information technology, in the direction of search algorithms for sustainable social progress.

The increasing role of the regions in addressing the challenges of modernization of Russia, against the backdrop of significant differentiation, chronic financial resources, labor imbalance determines the relevance of the search algorithms of steady progress. Not the last role in the solution of this problem to play model, reflecting the structure of the regional reproductive cycles, and thus developing understanding of the connection structure of the region and its system behavior. The solution of this problem can be found in the areas set out in Article improving mathematical apparatus studies of regional processes.