We study the properties of the chaotics introduced by Prof. V. V. Hrytsak. They are the most universal mathematical constructions of chaos and, contrary to all the others, expand the notion of chaos even to finite structures. We developed an algorithm of construction of the closure of the arbitrary chaotic set that can be efficiently used in evaluations of the propagation of autooscillatory waves. As examples, we consider the extension of epidemies and propaganda and the study of marketing. The notion of semimodular lattice, being a chaotic lattice element, is introduced, and the classification of chaotics is carried out. A class of chaotics, that is called "whirligig" and corresponds to granular chaotic structures, is proposed. The examples of quantities that are minimum by the amount of elements among all the others (whirligig, ant-hill, disorder, and quasimatroid) are given.

• Іглін Сергій Петрович (фізико-математичні науки)

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