519.87 Structural theory of complex systems. Geometric theory and humanitarian aspects of modeling

Brodsky Y. I. (ФИЦ ИУ РАН)

COMPLEX SYSTEMS, STRUCTURAL THEORY, MODEL SYNTHESIS, GEOMETRIC THEORY OF BEHAVIOR, FORMALIZATION OF SOCIAL SCIENCES


doi: 10.18698/2309-3684-2022-4-93113


We propose a formal definition of the complex system computer model, as a species of structure in the sense of N. Bourbaki — the M (Model) species of structure. The class of mathematical objects defined by the M species of structure has the following two properties: a complex created by combining mathematical objects of the M species of structure, according to the certain rules, is itself a mathematical object of the same M species of structure. The computation organization process is same for all the mathematical objects of the M species of structure and therefore can be implemented by a single universal program for the simulation calculations organization. The presence of these two properties of the M species of structure representatives allows us to build an end-to-end technology for the description, synthesis and software implementation of the complex systems models — Model Synthesis and Model-Oriented Programming. By studying the morphisms of the M species of structure base sets of the model constructed with the model synthesis help, and the invariants limiting such morphisms, we obtain a formal mathematical language for the study of complex open (changing their composition) systems. By conducting a traditional humanitarian discourse, one can always correlate it with the corresponding object of the M species of structure — translating the higher-level language of humanitarian concepts into mathematical language. The conclusions obtained using this language are, for example, that sustainable development is the modus vivendi of a complex open system and that in complex open systems, unlike closed physical systems, the conservation of laws plays a leading role (the system sacrifices power to maintain its axioms and structure), but not the conservation laws (which of course take a place).


Brodsky Yu.I. Structural theory of complex systems. Model synthesis. Mathematical Modeling and Computational Methods, 2022, no. 3, pp. 98–123.
Plato. Dialogi [Dialogues]. Moscow, Mysl Publ., 1986, 607 p.
Ershov Yu.L., Palyutin E.A. Matematicheskaya logika [Mathematical logic]. Moscow, Nauka Publ., 1987, 336 p.
Bohr N. Atomic physics and human knowledge. John Wiley & Sons Publ., 1958, 101 p.
Nicolis G., Prigogine I. Self-organization in nonequilibrium systems. New York, Wiley & Sons, 1977, 491 p.
Site of Sergei P.Kurdyumov "Synergetics" [Electronic resource], 2003. URL: https://spkurdyumov.ru/ (accessed: 29.05.2022)
Pavlovsky Yu.N. O sohranenii struktury vooruzhennyh sil v processe vooruzhennoj bor'by [On the preservation of the structure of the armed forces in the process of armed struggle]. Diskretnyj analiz i issledovanie operacij. Seriya 2 [Discrete analysis and operations research. Series 2], 1998, vol. 5, no. 1, pp. 40–55.
Brodsky Yu.I. Model'nyj sintez i model'no-orientirovannoe programmirovanie[Model synthesis and model-oriented programming]. Moscow, CC of RAS Publ., 2013, 142 p.
Korotaev A.V., Malinetsky G.G. Problemy matematicheskoj istorii: istoricheskaya rekonstrukciya, prognozirovanie, metodologiya [Problems of mathematical history: historical reconstruction, forecasting, methodology]. Moscow, URSS, 2016, p. 248.
Nalimov V.V. Veroyatnostnaya model' yazyka [Probabilistic model of language]. Moscow, Nauka Publ., 1979, 303 p.
Norden A.P. Ob osnovaniyah geometrii: sbornik klassicheskih rabot po geometrii Lobachevskogo i razvitiyu ee idej [On the foundations of geometry: a collection of classical works on Lobachevsky's geometry and the development of its ideas]. Moscow, Gostekhizdat Publ., 1956, 527 p.
Mishchenko A.S., Fomenko A.T. Kratkij kurs differencial'noj geometrii i topologii [A short course in differential geometry and topology]. Moscow, Fizmatlit Publ., 2004, 304 p.
The Overton Window  Mackinac Center [Electronic resource], 2019. URL: https://www.mackinac.org/ (accessed: 29.05.2022)
Brodsky Yu.I. Model'nyj sintez, kak podhod k geometricheskoj teorii povedeniya [Model synthesis as an approach to the geometric theory of behavior]. Modelirovanie, dekompoziciya i optimizaciya slozhnyh dinamicheskih processov[Modeling, decomposition and optimization of complex dynamic processes], 2019, vol. 34, no. 1 (34), pp. 43–71.
Burbaki N. Teoriya mnozhestv [Set theory]. Moscow, Mir Publ., 1965, 456 p.
Brodsky Yu.I. Popytka geometricheskoj klassifikacii etnokul'turnogo povedeniya [An attempt at geometric classification of ethno-cultural behavior]. Modelirovanie, dekompoziciya i optimizaciya slozhnyh dinamicheskih processov[Modeling, decomposition and optimization of complex dynamic processes], 2019, vol. 34, no. 1 (34), pp. 72–84.
Douglas M. How institutions think. New York, Syracuse University Press, 1986, 158 p.
Florensky P.A. Stolp i utverzhdenie istiny: opyt pravoslavnoj teodicei [The pillar and the affirmation of truth: the experience of orthodox theodicy]. Moscow, AST Publ., 2003, 635 p.
Krasnoshchekov P.S. Prostejshaya matematicheskaya model' povedeniya. Psihologiya konformizma [The simplest mathematical model of behavior. Psychology of conformity]. Mathematical Models and Computer Simulations, 1998, vol. 10, no. 7, pp. 76–92.
Kruglov L.V., Brodsky Yu.I. Model-oriented programming. Proceedings of CBU in Natural Sciences and ICT, 2021, vol. 2, pp. 63–67. DOI: 10.12955/pns.v2.154
Dimitrienko Yu.I. Mekhanika sploshnoy sredy. Tom 2. Universal'nye zako-ny mekhaniki i elektrodinamiki sploshnoj sredy [Continuum Mechanics. Vol. 2. Universal laws of continuum mechanics and electrodynamics]. Moscow, BMSTU Publ., 2011, 560 p.
Dimitrienko Yu.I., Dimitrienko O.Yu. Application of continuum mechanics methods for economy. IOP Journal of Physics: Conference Series, 2018, vol. 1141, art no. 012019. DOI: 10.1088/1742-6596/1141/1/012019


Бродский Ю.И. Структурная теория сложных систем. Геометрическая теория и гуманитарные ас-пекты моделирования. Математическое моделирование и численные методы, 2022, № 4, с. 93–113.



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