Otnositel'naya Metricheskaya Entropiya

V knige vvoditsya ponyatie otnositel'noy metricheskoy entropii zashumlennoy sistemy, znachenie kotoroy zavisit ot velichiny konechnogo masshtaba oshibki registratsii, kotoraya mozhet sluzhit' kriteriem stepeni peremeshivaniya v sisteme s shumom. Izlagaetsya teoriya fazovoy sinkhronizatsii kvaziperiodicheskikh avtokolebaniy vblizi rezonansa 1:1. V dannoy rabote pokazano, chto v osnove mekhanizma poteri sinkhronizatsii avtokolebaniy takogo tipa lezhat sedlo-uzlovye bifurkatsii invariantnykh krivykh, chto sootvetstvuet kasatel'nym bifurkatsiyam sedlovykh i prityagivayushchikh torov v polnoy sisteme, ustanovlennym ranee. Pokazano, chto yavleniya sinkhronizatsii i stokhasticheskogo rezonansa privodyat k snizheniyu stepeni peremeshivaniya v zashumlennykh sistemakh. Pri etom v sluchae sinkhronizatsii periodicheskikh i kvaziperiodicheskikh avtokolebaniy shum fiksirovannoy intensivnosti okazyvaet bol'shee peremeshivayushchee deystvie na predel'nyy tsikl, lezhashchiy na poverkhnosti tora, chem na predel'nyy tsikl, ne yavlyayushchiysya rezonansom na tore. Dannyy vyvod spravedliv i dlya torov: shum vyzyvaet bol'shee peremeshivanie v sluchae, esli rezhimu kolebaniy sistemy sootvetstvuet ergodicheskiy tor, otvechayushchiy rezonansu na tore bol'shey razmernosti.