Measurement of the status of complex systems in multidimensional phase spaces

Abstract

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