Panasjuk M.V., Pudovik E.M.

Казанский государственный университет


Authors are offering the new approach and methods for analysis of territorial system stability problems decision which connect an estimation of development stability with an integrated estimation of the system condition quality dynamics in view of the preset levels of the condition estimation.


Scientifically methodical basis of the condition estimation and its stability are procedures for mathematical classification of territorial system elements. The basic methodological precondition of the analytical problems decision is a statement that allocated on the basis of values of the indicators classes preset complex and corresponding to them subsets of elements characterize the definite quality of element condition, and all classification system characterizes quality of the analyzed territory condition.


Basic features of the classification approach to an estimation of territorial system condition stability are:

  1. The analysis of stability on the basis of a system displayed attributes of similarity measures.
  2. Comparison of element class to the certain quality of systems condition (level of estimation).
  3. Connection of subjective and impartial assessments in the classification analysis.
  4. Estimation of steadiness/stability by the analysis of transitions from a class/group in a class of elements.

The considered approach to the analysis of development stability assumes fulfillment of following conditions:

  • Number of estimation levels should not vary during all observable period; otherwise results of estimations comparison for different years will be non-comparable.
  • Classes/groups of analyzed elements of territorial system with different levels of an estimation form not crossed sets, i.e. the condition of each element has an unequivocal estimation.
  • Method of classification should be uniform for all intervals of analyzed period time of the without dependence from character of their dynamics.

Development of the given approach has enabled definitions for some parameters of the territorial development dynamics analysis, and also its stability. Characteristics, in particular, concern to them: The maximal frequency of occurrence for estimation a level, number of transitions from a level to a level, factor of instability, measures of the system condition stability degree estimation, etc.


One of the approach basic features is its direct orientation on realization in GIS environment, the territory geoinformation analysis. The given direction in many respects has caused development of methodical base, structure of indicator system, measures and parameters of the territorial system stability estimation. Realization of the approach in GIS environment leans on bases of spatial data, a complex of GIS-maps and the specialized software package including both estimation and analytical procedures, and procedures of the GIS-analysis. Results of the problems decision represent a complex of GIS-maps and explanatory documents. Thus, the given approach creates bases for development of GIS special analytical functions for the decision of monitoring and the analysis of territorial system problems.


Since 1998 the approach is successfully applied at the decision of scientific and industrial problems of the stability analysis of the Republic of Tatarstan territorial system, including the analysis of development stability of city settlements, administrative regions systems, the operative (monthly) analysis of republic system social and economic condition dynamics, an estimation of competitive positions of Kazan stability, etc.