Modeli mikroekonomske dinamike: algoritmi bifurkacije i ponašanja složenih sistema

DOI: https://doi.org/10.5937/vojtehg72-52213
Ključne reči: dinamika sistema ponude i potražnje, vremensko kašnjenje, granični ciklus, bifurkacija, haos

Sažetak


Uvod/cilj: Proučavanje dinamike uzajamnog uticaja ponude i potražnje važno je kada je reč o finansijskim gubicima usled neizvesne potražnje i grešaka u predviđanju. Cilj rada jeste da kreira matematički model dinamike ove interakcije za tržište jednog proizvoda.

Metode: U radu se predlaže matematički model stanja sistema ponude i potražnje unutar okvira u kojem se razmatraju procesi koji deluju u ovom sistemu sa aspekta metodologije ekonomske sinergije. Matematički model dinamike ima oblik sistema dve diferencijalne jednačine sa kvadratnom nelinearnošću.

Rezultati:Korišćenje predloženog modela za reprodukciju različitih dinamičkih stanja procesa tržišne samoregulacije omogućilo je identifikaciju hijerarhije prelaska iz stabilnih dinamičkih režima u nestabilne sa pojavom odgovarajućih bifurkacija. Najviše pažnje posvećeno je proučavanju ponašanja sistema na granicama oblasti stabilnosti.

Zaključak: Otkriveno je postojanje bifurkacije sedlo-čvor graničnih ciklusa što ukazuje na pojavu autooscilacija koje su stabilne u slučaju „mekog” ciklusa, a nestabilne u slučaju „tvrdog” ciklusa. Prilikom proučavanja bifurkacije kodimenzije 2 –  „dvostruka nula”  otkrivene su specijalne dinamičke strukture, određene svojstvima opštih bifurkacija. Ova vrsta ponašanja karakteriše se autooscilacijama niske frekvencije što dovodi do takozvanih „ultradugih” talasa ekonomskog stanja.

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Objavljeno
2024/11/17
Broj časopisa
Vol. 72 Br. 4 (2024): oktobar - decembar
Rubrika
Originalni naučni radovi

Sva prava zadržana (c) 2024 Lyudmyla Malyarets, Oleksandr Dorokhov, Anatoly Voronin, Irina Lebedeva, Stepan Lebedev

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