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## Fractal analysis of Hopf bifurcation at infinity

Radunović, Goran; Žubrinić, Darko; Županović, Vesna
Fractal analysis of Hopf bifurcation at infinity // International journal of bifurcation and chaos in applied sciences and engineering, 22 (2012), 12; 1230043-1 doi:10.1142/S0218127412300431 (međunarodna recenzija, članak, znanstveni)

Naslov
Fractal analysis of Hopf bifurcation at infinity

Autori
Radunović, Goran ; Žubrinić, Darko ; Županović, Vesna

Izvornik
International journal of bifurcation and chaos in applied sciences and engineering (0218-1274) 22 (2012), 12; 1230043-1

Ključne riječi
Spiral; box dimension of unbounded sets; Minkowski content; planar vector field; Hopf–Takens bifurcation at infinity

Sažetak
Using geometric inversion with respect to the origin, we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann sphere. We study its basic properties, and apply it to the study of the Hopf–Takens bifurcation at infinity. We show that for any given phase portrait $\mathcal P$ of a polynomial vector field there exists a constructive polynomial vector field such that its phase portrait is obtained from $\mathcal P$ by geometric inversion with respect to the origin.

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti

Napomena

Projekt / tema
036-0361621-1291 - Nelinearna analiza diferencijalnih jednadžbi i dinamičkih sustava (Mervan Pašić, )
036-0361621-3012 - Napredne strategije upravljanja i estimacije u složenim sustavima (Nedjeljko Perić, )

Ustanove
Fakultet elektrotehnike i računarstva, Zagreb

#### Časopis indeksira:

• Current Contents Connect (CCC)
• Web of Science Core Collection (WoSCC)
• Science Citation Index Expanded (SCI-EXP)
• SCI-EXP, SSCI i/ili A&HCI
• Scopus

• MathSciNet