APPLICATIONS OF THE TOPOLOGICAL ROUGHNESS METHOD TO RESEARCH IN SOCIOSYNERGETICS

Abstract

    Rassmatrivayetsya voprosy samoorganizatsii v sotsial'nykh sistemakh ili sotsiosinergetiki. Kratko privedeny osnovy metoda topologicheskoy grubosti, kotoryy pozvolyayet issledovat' grubost' i bifurkatsii sinergeticheskikh sistem samoy razlichnoy fizicheskoy prirody. V rabotakh avtora metod ispol'zovan dlya issledovaniy izvestnykh sinergeticheskikh sistem i khaosa: attraktory Lorentsa i Resslera, sistem Chua, Belousova-Zhabotinskogo, «khishchnik-zhertva-pishcha», Khenona, Kaldora, Shumpetera, bifurkatsii Khopfa i dr. Metod topologicheskoy grubosti sistem, predpolagayet formalizovannost' matematicheskoy modeli issleduyemykh sistem. V sluchaye slabo formalizuyemykh i ne formalizuyemykh matematicheskimi modelyami sistem, predlagayetsya primeneniye podkhoda analogiy teoretiko-mnozhestvennoy topologii i abstraktnogo metoda k issledovaniyam takikh sistem, kotoryye sozdayut osnovy dlya ispol'zovaniya metoda topologicheskoy grubosti k sotsial'nym sistemam v chastnosti, kak k slozhnym sinergeticheskim sistemam. Ещё         951 / 5 000 The article considers the issues of self-organization in social systems or sociosynergetics. The article briefly presents the basics of the topological roughness method, which allows us to study the roughness and bifurcations of synergetic systems of various physical natures. In the author's works, the method is used to study known synergetic systems and chaos: Lorenz and Ressler attractors, Chua, Belousov-Zhabotinsky, "predator-prey-food" systems, Henon, Kaldor, Schumpeter, Hopf bifurcations, etc. The method of topological roughness of systems assumes the formalization of the mathematical model of the systems under study. In the case of systems that are weakly formalized and not formalized by mathematical models, it is proposed to apply the approach of analogies of set-theoretical topology and the abstract method to studies of such systems, which create the basis for using the topological roughness method to social systems in particular, as complex synergetic systems.