Measurement of the status of complex systems in multidimensional phase spaces
Keywords:
complex systems, temporal data arrays, multidimensional phase spaces, state equations, measuring scalesAbstract
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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