• Gennadiy V. Averin
  • Anna V. Zviagintseva
  • Igor S. Konstantinov
  • Angela A. Shvetsova
Keywords: complex systems, temporal data arrays, multidimensional phase spaces, state equations, measuring scales


It is proposed to use the principle of corresponding states and the principle of distance invariance in multidimensional phase spaces to create models of systems of various nature based on experimental or statistical information presented in the form of temporal data. This scientific idea is closely connected with the logical construction of measuring scales in natural science, and, in particular, in thermodynamics. A method for complex measurement of the state of objects in relation to the reference state and the reference process has been developed, based on obtaining state equations in the form of phenomenological relationships and using multidimensional scaling methods. As examples, the equations of states are obtained and measuring scales for two complex systems are constructed. The first example is related to the study of the similarity of biological species in the three-dimensional phase space of state variables. The second example uses statistical data on the state and development of Russian cities. The measuring scale is also constructed for the three-dimensional phase space of socio-economic variables. The proposed approach is universal and can be used for a comprehensive assessment of the development processes of countries, regions and cities, the study of human development and ranking of socio-economic objects by a set of indicators, while analyzing the environmental pollution by indicators of environmental safety, studying the similarity of objects of one class for several variables and etc.


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. Averin, G.V., 2014. System dynamics. Donetsk, Donbass, Pages: 405. Available at: (accessed 24 April, 2019). (in Russian).

. Zviagintseva, A.V., 2016. Probabilistic Methods of a Complex Assessment of Natural and Anthropogenic Systems. Cpektr Publishing House, Russia, Moscow, Pages: 257. Available at: (accessed 24 April, 2019). (in Russian).

. Averin, G.V., Konstantinov, I.S., Zviagintseva, A.V., 2016. On the Continual Approach to the Model Data Presentation. Bulletin of Computer and Information Technologies, 10: 47–52. (in Russian).

. Zviagintseva, A.V., Averin ,G.V., 2016. Integration of the several multivariate Pfaff equations which are important in application. Scientific Bulletin of Belgorod State University. Series. Mathematics. Physics, 27(248). Issue 45: 102–114. (in Russian).

. Averin, G.V., Konstantinov, I.S., Zviagintseva, A.V., Tarasova, O.A., 2015. The Development of Multi-Dimensional Data Models Based on the Presentation of an Information Space as a Continuum. International Journal of Soft Computing, 10(6): 458–461.

. Averin, G.V., Zviagintseva, A.V., Shevtsova, M.V., Кurtova, L.N., 2017. On Representation of Discrete Information of Temporal Databases in the Continuous Form. Journal of Engineering and Applied Sciences, 12 (15): 3884–3889, DOI: 10.3923/jeasci.2017.3884.3889.

. Averin, G.V., Zviagintseva, A.V., Konstantinov, I.S., Shvetsova, Ð.Ð., 2018. ForeÑasting indicators of territorial entity based on phenomenological models of collective behavior. Ðmazonia investiga, 7(13): 42–49.

. Averin, G.V., Zviagitrseva, A.V., 2017. On justice of the principle of corresponding conditions for various systems. Scientific Bulletin of Belgorod State University. Series. Economy. Computer science, 16(265). Issue 43: 104–112. Available at: (accessed 15.09.2018). (in Russian).

. Kostenko, B.B., Kuznetsov, S.D., 2019. History and actual problems of temporal databases. Citforum. URL: (accessed 24 April, 2019).

. Gukhman, A.A., 1986. About the thermodynamic bases. Moscow, Energoatomizdat, 383 (In Russian).

. Roberts, J.K., Miller, A.R., 1951.Heat and Thermodynamics. 4th ed. Blackie, London, 274 p.

. AnAge: The Animal Ageing and Longevity Database. Available at: (accessed 24 April, 2019).

. Database of the Federal State Statistics Service [Electronic source] URL: (accessed 7 April, 2019).

How to Cite
Averin, G. V., Zviagintseva, A. V., Konstantinov, I. S., & Shvetsova, A. A. (2019). MEASUREMENT OF THE STATUS OF COMPLEX SYSTEMS IN MULTIDIMENSIONAL PHASE SPACES. COMPUSOFT: An International Journal of Advanced Computer Technology, 8(6). Retrieved from