Phenomenological relations for the continual state spaces in various nature systems

Author(s):  S.G. Ehilevsky, Polotsk State University, Novopolotsk, Republic of Belarus, ekhilevskiy@mail.ru

G.V. Averin, Dr., Prof., Belgorod National Research University, Belgorod, Russia, averin@bsu.edu.ru

I.S. Konstantinov, Belgorod National Research University, Belgorod, Russia, konstantinov@bsu.edu.ru

А.V. Zviagintseva, candidate of Sciences, associate Professor, Belgorod National Research University, Belgorod, Russia, zviagintseva@bsu.edu.ru

Issue:  Volume 44, №23

Rubric:  System analysis and processing of knowledge

Annotation:  It was proposed to use scalar empirical measures associated with continuous representations in system state spaces to model complex systems. A method for analyzing observational data has been developed, which is based on the probabilistic nature application measure, determined on the set of events identified by a given feature. A special method feature is the representation of the state of objects through joint events of simultaneous observation of the values of state variables and obtaining empirical dependencies on the basis of experimental data. The proposed method was used to study information on the chemical elements of the Mendeleev periodic system and their basic properties, data on the indices of vertebrates biological species and information from the Federal Statistics Service on the Russian cities development state. These examples show the possibility of finding the equations of states in the form of probability distributions and relationships in the form of dependencies that reflect the balance principles for a measure as a continual value. Equations and dependences of a sufficiently high quality are obtained, which indicate the validity of the application of conservation principles in relation to the state spaces of complex systems. The results of the data analysis characterizing the physical, biological and socio-economic systems, indicate the possibility of using basic science-based principles in the study of different nature complex systems

Keywords:  complex systems, arrays of experimental data, state spaces, phenomenological models, equations of states, conservation principles

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