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master's thesis
Kaotične oscilacije u nelinearnom električnom titrajnom krugu
Zagreb: University of Zagreb, Faculty of Science, 2020. urn:nbn:hr:217:390752
Subotić, Hrvoje
University of Zagreb
Faculty of Science
Department of Physics

Institutional repository: Repository of the Faculty of Science

Cite this document

Subotić, H. (2020). Kaotične oscilacije u nelinearnom električnom titrajnom krugu (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:390752

Subotić, Hrvoje. "Kaotične oscilacije u nelinearnom električnom titrajnom krugu." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:390752

Subotić, Hrvoje. "Kaotične oscilacije u nelinearnom električnom titrajnom krugu." Master's thesis, University of Zagreb, Faculty of Science, 2020. https://urn.nsk.hr/urn:nbn:hr:217:390752

Subotić, H. (2020). 'Kaotične oscilacije u nelinearnom električnom titrajnom krugu', Master's thesis, University of Zagreb, Faculty of Science, accessed 22 July 2024, https://urn.nsk.hr/urn:nbn:hr:217:390752

Subotić H. Kaotične oscilacije u nelinearnom električnom titrajnom krugu [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2020 [cited 2024 July 22] Available at: https://urn.nsk.hr/urn:nbn:hr:217:390752

H. Subotić, "Kaotične oscilacije u nelinearnom električnom titrajnom krugu", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2020. Available at: https://urn.nsk.hr/urn:nbn:hr:217:390752

Metadata
TitleKaotične oscilacije u nelinearnom električnom titrajnom krugu
Title (english)Chaotic oscillations in a non-linear electric oscillating circuit
AuthorHrvoje Subotić
MentorEmil Tafra (mentor)
Committee memberEmil Tafra (predsjednik povjerenstva)
Committee memberDanko Radić (član povjerenstva)
Committee memberMaja Planinić (član povjerenstva)
Committee memberMatko Milin (član povjerenstva)
Committee memberKatarina Jeličić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Physics)
Zagreb
Defense date and country2020-03-20, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Physics
Abstract
Uvođenjem diode kao nelinearnog elementa u električni titrajni krug, uspjeli smo ga dovesti u režim kaotičnih oscilacija. Sastavili smo dva RLD kruga s različitim zavojnicama i pratili smo postupan prelazak sustava u kaotično ponašanje na tri načina: vremenskim prikazom, X-Y prikazom i pomoću frekvencijskog spektra. U oba RLD kruga potvrdili smo teorijska predviđanja i vidjeli kada se u takvom sustavu pojavljuju bifurkacije, kaotično ponašanje i otoci reda. Jedna od važnijih značajki kaotičnih sustava je univerzalnost koja se može očitovati i u Feigenbaumovoj konstanti. Izračunata je Feigenbaumova konstanta za oba RLD kruga; za RLD krug sa zavojnicom induktiviteta 2/3 mH dobili smo vrijednost Feigenbaumove konstante δ_1 = 3.61, a za RLD krug sa zavojnicom induktiviteta 2 mH dobili smo δ_2 = 3.79. Oba ova rezultata odstupaju od teorijske vrijednosti δ = 4.669, ali ta je vrijednost dobivena kada promatramo uzastopne bifurkacije visokog reda. Da bi se mogla preciznije izmjeriti Feigenbaumova konstanta, potreban je drugačiji eksperimentalni postav koji će biti u stanju razlučiti više bifurkacije.
Abstract (english)
By introducing a diode as a non-linear element in the electrical oscillating circuit, we have succeeded to bring it to the state of the chaotic oscillations. We have constructed two RLD circuits with different inductors and followed a gradual transition into a chaotic behaviour in three ways: waveform, X-Y display and frequency spectrum. In both RLD circuits we have confirmed theoretical hypothesis and seen when would we in such systems observe bifurcations, chaotic behaviour and island of order. One of more important features of chaotic systems is universality which can be manifested in Feigenbaum constant. We have calculated the Feigenbaum constant for both RLD circuits; for RLD circuit with inductor of inductance 2/3 mH we have calculated the value of Feigenbaum constant of δ_1 = 3.61 and for RLD circuit with inductor of inductance 2 mH we got δ_2 = 3.79. Both values differ from theoretical value of Feigenbaum constant δ = 4.669, but this value is calculated when we observe successive bifurcations of higher order. In order to be more precise in measurement of Feigenbaum constant, we need different experimental setup that would be able to identify bifurcations of higher order.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:390752
Study programmeTitle: Physics; specializations in: Education
Course: Education
Study programme type: university
Study level: integrated undergraduate and graduate
Academic / professional title: magistar/magistra edukacije fizike (magistar/magistra edukacije fizike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2020-08-20 12:36:25