Naslov
Fractal analysis of canard cycles with two breaking parameters and applications

Autori
Huzak, Renato ; Vlah, Domagoj

Izvornik
Communications on Pure & Applied Analysis (1553-5258) 18 (2019), 2; 959-975

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
box dimension ; canard cycles ; singular perturbation theory ; slow divergence integral ; Tricot method

Sažetak
In previous work [13] we introduced a new box dimension method for computation of the number of limit cycles in planar slow-fast systems, Hausdorff close to balanced canard cycles with one breaking mechanism (the Hopf breaking mechanism or the jump breaking mechanism). This geometric approach consists of a simple iteration method for finding one orbit of the so-called slow relation function and of the calculation of the box dimension of that orbit. Then we read the cyclicity of the balanced canard cycles from the box dimension. The purpose of the present paper is twofold. First, we generalize the box dimension method to canard cycles with two breaking mechanisms. Second, we apply the method from [13] and our generalized method to a number of interesting examples of canard cycles with one breaking mechanism and with two breaking mechanisms respectively.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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