Існування рівноважних станів у динамічних системах із притягальною взаємодією
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Date
2018
Authors
Лемешко, Єлизавета
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Abstract
Поняття iнтерактивної складної системи є основним iнструментом у побудовi математичних
моделей для розв’язання сучасних проблем цивiлiзацiйного розвитку. Таким, зокрема, є поняття складної
динамiчної системи з притягальною взаємодiєю. Проблема пошуку та досягнення компромiсного стану
для опонентiв на спiльнiй територiї iснування має рiзнi варiанти постановки задачi i вибору конфлiктної взаємодiї. У цiй роботi сформульовано та доведено теорему про iснування граничного стану в
динамiчнiй системi з притягальною взаємодiєю в термiнах щiльностей.
Nowadays, science is characterized by needs of the study of various complex processes and phenomena’s. Today’s research of complex and dynamical systems is one of the most advanced ways of research and evolution of the modern world. Models of biology and ecology, physical models, various economic and social models are typical examples of dynamic systems. The concept of an interactive complex system in modern science is a main tool for construction of mathematical models for solving modern civilization problems and development. The dynamical systems approach to conflict is relatively new, but it has beginning in different research fields. Theory of dynamic systems helps us to understand the experiments, build the mathematical model of iterations and examine behavior and relations between opponents, like distribution of resources and territory, population growing etc. This is a challenging problem of finding and achieving a compromise state for opponents on a common territory has different options to define the task and to choose conflict interaction. In 2016, the monograph by V. Koshmanenko where was introduced new approach for dynamic system of conflict that based on interactions of the opponents in the form probability distribution in the disputed area was published. In particular, presented the concept of a complex dynamic system with attractive interaction. The relevance of this research is improving new dynamical system and researching for a new application of abstract models in everyday life. In this paper briefly fundamentals of the theory of dynamical systems described and the theorem on the existence of a equilibrium state in a the new, perspective for research, dynamical system with attractive interaction in terms of probability distributions (measures) and their densities, formulated and proved.
Nowadays, science is characterized by needs of the study of various complex processes and phenomena’s. Today’s research of complex and dynamical systems is one of the most advanced ways of research and evolution of the modern world. Models of biology and ecology, physical models, various economic and social models are typical examples of dynamic systems. The concept of an interactive complex system in modern science is a main tool for construction of mathematical models for solving modern civilization problems and development. The dynamical systems approach to conflict is relatively new, but it has beginning in different research fields. Theory of dynamic systems helps us to understand the experiments, build the mathematical model of iterations and examine behavior and relations between opponents, like distribution of resources and territory, population growing etc. This is a challenging problem of finding and achieving a compromise state for opponents on a common territory has different options to define the task and to choose conflict interaction. In 2016, the monograph by V. Koshmanenko where was introduced new approach for dynamic system of conflict that based on interactions of the opponents in the form probability distribution in the disputed area was published. In particular, presented the concept of a complex dynamic system with attractive interaction. The relevance of this research is improving new dynamical system and researching for a new application of abstract models in everyday life. In this paper briefly fundamentals of the theory of dynamical systems described and the theorem on the existence of a equilibrium state in a the new, perspective for research, dynamical system with attractive interaction in terms of probability distributions (measures) and their densities, formulated and proved.
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Keywords
компромiс, опоненти, притягальна взаємодiя, конфлiкт, щiльнiсть, динамiчна система, оптимальнiсть, граничний стан, стаття, compromise, opponents, attractive interaction, conflict, density, dynamical system, optimality, boundary condition
Citation
Лемешко Є. І. Існування рівноважних станів у динамічних системах із притягальною взаємодією / Лемешко Є. І. // Могилянський математичний журнал : науковий журнал. - 2018. - Т. 1. - С. 21-24.