eb454998-68e7-4ef0-b9f0-8b5f4c0eb74a20210318034421586wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON SYSTEMS AND CONTROL1991-876310.37394/23203http://wseas.org/wseas/cms.action?id=4073220202022020201510.37394/23203.2020.15http://wseas.org/wseas/cms.action?id=23195Elements of Geometric Theory of Complex Systems BehaviorYury I.BrodskyDorodnicyn Computing Centre, Federal Research Centre “Computer Science and Control” of RAS, Moscow, RUSSIAN FEDERATIONThe paper proposes the elements of a geometric theory of behavior. The basis of this theory is Model Synthesis - an end-to-end technology for describing, synthesizing and implementing agent models. Its main achievement – is the formalization of an agent by a mathematical object - a species of structure in the sense of N. Bourbaki. Algorithms that implement actions of agents are included in the base sets of this species of structure. Let us consider morphisms of the base sets with the special attention to the actions mappings. It occurs that unrestricted mappings of base sets can radically change system’s behavior. We can use invariants as restrictions of mappings, if demand their preservation under admissible morphisms. As a result, we can obtain a classification of the systems behavior depending on the invariants that persist during the mappings.228202022820201929https://www.wseas.org/multimedia/journals/control/2020/a065103-064.pdf10.37394/23203.2020.15.3http://www.wseas.org/multimedia/journals/control/2020/a065103-064.pdfN. P. Buslenko, Complex systems and simulation models, Cybernetics, Vol. 12, No 6, 1976, pp. 862-870. I. Prigogine, G. Nicolis, Self-Organization in Non-Equilibrium Systems, Wiley, 1977. N. Bourbaki, Elements of Mathematics. Theory of Set, Springer, 2004. 10.1134/s0965542515010054Yu. I. Brodsky, Bourbaki's Structure Theory in the Problem of Complex Systems Simulation Models Synthesis and Model-Oriented Programming, Computational Mathematics and Mathematical Physics, Vol. 55, No 1, 2015, pp. 148-159. Yu. I. Brodsky, Model synthesis and model-oriented programming – the technology of design and implementation of simulation models of complex multicomponent systems, In the World of Scientific Discoveries, Series B, Vol. 2, No 1, 2014, pp. 12-31. 10.1126/science.aau8712A. Cohn, M. A. Maréchal, D. Tannenbaum, C. L. Zünd, Civic honesty around the globe, Science, Vol. 365, No 6448, 2019, pp. 70-73. DOI:10.1126/science.aau8712. F. Klein, A comparative review of recent researches in geometry,https://arxiv.org/abs/0807.3161, last accessed 2019/12/11. S. Mac Lane, Categories for the Working Mathematician, Springer, 1998. S. Foldes, Fundamental Structures of Algebra and Discrete Mathematics, John Wiley & Sons, 1994. 10.1177/0268580919839649Yu. I. Brodsky, On Mathematical Modeling in the Humanities, Power, Violence and Justice: Reflections, Responses and Responsibilities. View from Russia: collected papers XIX ISA World Congress of Sociology (Toronto, Canada, July 15-21, 2018), Moscow: RSS; FCTAS RAS, 2018, pp. 46-64. A brief explanation of the Overton window, Mackinac Center for Public Policy, https://www.mackinac.org/OvertonWindow, last accessed 2019/12/11. Yu. N. Pavlovsky, Fundamentals of mathematical modeling for complex systems, In: System Analysis and Modeling of Integrated World Systems. Vol. 1, EOLSS Publishers Co. Ltd, 2009, pp. 221-234. 10.2307/j.ctv346s0kP. A. Florensky, The Pillar and Ground of the Truth: An Essay in Orthodox Theodicy in Twelve Letters, Princeton (NJ) University Press, 2004. M. Douglas, How Institutions Think, Syracuse (NY) University Press, 1986. 10.4135/9781529714708.n1Yu. I. Brodsky, Russia – the West or the East? Mathematical Models and Humanitarian Analysis, The Futures We Want: Global Sociology and the Struggles for a Better World. View from Russia: collected papers. The 3rd ISA Forum of Sociology “The Futures We Want: Global Sociology and the Struggles for a Better World”, Moscow: RSS, 2016, pp. 53-59.