V. A. Kim, R. I. Parovik, “Investigation of forced oscillations of a Duffing oscillator with a variable fractional order derivative”, News of the Kabardino-Balkarian Scientific Center of the Russian Academy of Sciences, 2020, Issue 1,Pages <nobr>46

This article is cited in 2 papers

PHYSICAL-MATHEMATICAL SCIENCES

Investigation of forced oscillations of a Duffing oscillator with a variable fractional order derivative

V. A. Kim^abc, R. I. Parovik^ad

^a Vitus Bering Kamchatka State University, 683032, Petropavlovsk-Kamchatsky, Pogranichnaya street, 4
^b Institute of Applied Mathematics and Automation – branch of the FSBSE "Federal Scientific Center "Kabardin-Balkar Scientific Center of the Russian Academy of Sciences", 360000, KBR, Nalchik, Shortanov street, 89 A
^c Kamchatka State Technical University, 683003, Petropavlovsk-Kamchatsky, st. Klyuchevskaya, 35
^d Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, 684034, Kamchatka Territory, Yelizovsky District, v. Paratunka, Mirnaya street, 7

Abstract: A mathematical model of a Duffing type oscillator with a variable fractional derivative of the Riemann-Liouville derivative is studied. Using the harmonic balance method, algorithms for constructing amplitude-phase characteristics were found. The amplitude-frequency and phase-frequency characteristics were built. The inverse dependence of the Q factor on the order of the fractional derivative is shown. The Q-factor surfaces are constructed depending on the frequency and amplitude.

Keywords: Riemann-Liouville derivative, Grunwald-Letnikov derivative, oscillograms, phase trajectories, amplitude-frequency characteristic (AFC), phase-frequency characteristic (PFC).

UDC: 517.98; 517.2

Received: 11.02.2020

DOI: 10.35330/1991-6639-2020-1-93-46-56