Stokhasticheskie attraktory

Vzaimodeystvie mezhdu sluchaynymi vozmushcheniyami i nelineynost'yu sootvetstvuyushchikh dinamicheskikh modeley igraet vazhnuyu rol' v ponimanii novykh yavleniy v mekhanike, radiofizike, biologii. Vblizi tochek bifurkatsiy, gde attraktory imeyut vysokuyu chuvstvitel'nost' k vozmushcheniyam, nablyudayutsya transformatsii stokhasticheskikh attraktorov. Klyuchevuyu rol' v ponimanii veroyatnostnykh mekhanizmov takikh yavleniy igraet analiz stokhasticheskoy chuvstvitel'nosti attraktorov. V rabote predstavlen matematicheskiy apparat i tekhnika funktsiy stokhasticheskoy chuvstvitel'nosti (FSCh) dlya diskretnykh dinamicheskikh sistem. Metod FSCh pozvolyaet provodit' konstruktivnyy veroyatnostnyy analiz stokhasticheskikh attraktorov i ikh bifurkatsiy. Vozmozhnosti tekhniki FSCh detal'no illyustriruyutsya na klassicheskikh modelyakh Ferkhyul'sta i Eno v zonakh perekhoda ot poryadka k khaosu. Znachitel'noe vnimanie udelyaetsya issledovaniyu obratnykh stokhasticheskikh bifurkatsiy. Dannaya tekhnika pozvolyaet naryadu s analizom stokhasticheskikh attraktorov reshat' vazhnuyu zadachu ikh sinteza. V rabote izlagaetsya novyy podkhod k resheniyu zadachi upravleniya veroyatnostnymi kharakteristikami stokhasticheskikh dinamicheskikh rezhimov s prilozheniem k probleme strukturnoy stabilizatsii i podavleniya khaosa.