and Computational Methods

doi: 10.18698/2309-3684-2021-4-12134

We consider a discrete analog of the classical A. Lotka – V. Volterra competition model in the environment of cellular automata. In the classical model, we know that the type of its evolution over time primarily depends on the coefficients of double standards affiliation to certain ranges of their possible values. The paper shows that the same situation holds for the discrete model either. We can see there is a soft power effect for the classical model. The classic competition model turns into a cooperative positional differential game, the limitations of which are the original system of competition equations by A. Lotka – V. Volterra. The controls are the coefficients of double standards when considering it concerning social systems. The effect of soft power is that the parties tend to compare the competitive pressure on them by the rival population with the one within the domestic population and may take the less stress of the opponent for his favorable attitude towards them, and more extensive — for the hostile manifestation. Whereas comparing the external competitive pressure with the internal pressure in this game does not give us any information — everything depends exclusively on the coefficients of double standards, which are controls and therefore are unavailable to the opponents in this game. Simulation experiments with the discrete analog of the competition model implemented in the cellular automata environment show that the effect of soft power also takes place in this case

Бобров В.А., Бродский Ю.И. Моделирование клеточными автоматами эффектов двойных стандартов и мягкой силы при конкуренции. Математическое моделирование и численные методы, 2021, № 4, с. 121–134.

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).

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

doi: 10.18698/2309-3684-2022-3-98123

The purpose of this work is to organize from a unified viewpoint the results of the author's work in the field of the structural theory of complex systems modeling and the practice of their implementing of the last two decades. We propose a formal definition of the complex system computer model, as a species of structure in the sense of N. Bourbaki — the М (System) species of structure, based on the humanitarian analysis of the complex systems key properties, recognized by a number of authoritative researchers and practicians in this field, and the assumption of the possibility of constructing a mathematical computer model of a complex system, — the closure hypothesis. The class of mathematical objects defined by the М species of structure has the following two properties: a complex created by combining a finite number of mathematical objects of the М species of structure, according to the certain rules, is itself a mathematical object of the same М species of structure. The computation organization process is same for all the mathematical objects of the М 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 М 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 М 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 М species of structure — translating the higher-level language of humanitarian concepts into mathematical language. The proposed theory has a practical application in the field of development, description and implementation of complex software systems. A new programming paradigm is proposed — Model-Oriented Programming, which is a complete implementation of CAD methods in programming. When developing a software system, it is possible to stay within the framework of declarative programming, avoiding imperative, which greatly simplifies both its development and implementation, and subsequent debugging.

Бродский Ю.И. Структурная теория сложных систем. Модельный синтез. Математическое моделирование и численные методы, 2022, № 3, с. 98–123.