Il'dar Sharafutdinov

Bifurkatsiya Khopfa V Negladkikh Dinamicheskikh Sistemakh: Priblizhennye Metody I Algoritmy Chislennogo Issledovaniya Il'dar Sharafutdinov Russian edition

V knige rassmatrivayutsya nekotorye klassy negladkikh dinamicheskikh sistem, dlya kotorykh predlagayutsya priblizhennye metody issledovaniya ikh bifurkatsionnogo povedeniya v okrestnostyakh nepodvizhnykh tochek. Osnovnoe vnimanie udeleno bifurkatsii Khopfa, nazyvaemoy takzhe bifurkatsiey Andronova-Khopfa ili bifurkatsiey rozhdeniya tsikla. V nastoyashchee vremya raboty, posvyashchennye issledovaniyu negladkikh sistem, imeyut v osnovnom prikladnuyu napravlennost', a predlagaemye v nikh metody nosyat evristicheskiy kharakter. Dannaya rabota prizvana chastichno vospolnit' etot probel. V knige izuchayutsya dinamicheskie sistemy, gladkost' kotorykh narushaetsya na nekotorom mnogoobrazii fazovogo prostranstva. Vyvodyatsya priznaki bifurkatsii Khopfa, asimptoticheskie formuly dlya rozhdayushchikhsya tsiklov i priznak ikh ustoychivosti. Izuchaetsya takzhe sluchay, kogda sistema yavlyaetsya gladkoy tol'ko v nekotorom podmnozhestve fazovogo prostranstva. Kniga prednaznachena dlya studentov, aspirantov, prepodavateley i nauchnykh rabotnikov.