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).
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