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Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, 2004, Number 3, Pages 71–90
(Mi basm180)
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This article is cited in 7 scientific papers (total in 7 papers)
Research articles
Variety of the center and limit cycles of a cubic system, which is reduced to lienard form
Yu. L. Bondar, A. P. Sadovskii Belarussian State University, Minsk, Belarus
Abstract:
In the present work for the system $\dot{x}=y(1+Dx+Px^2)$, $\dot{y}=-x+Ax^2+3Bxy+Cy^2+Kx^3+3Lx^2y+Mxy^2+Ny^3$ 25 cases are given when the point $O(0,0)$ is a center. We also consider a system of the form $\dot{x}=yP_0(x)$, $\dot{y}=-x+P_2(x)y^2+P_3(x)y^3$, for which 35 cases of a center are shown. We prove the existence of systems of the form $\dot{x}=y(1+Dx+Px^2)$, $\dot{y}=-x+\lambda y +Ax^2+Cy^2+Kx^3+3Lx^2y+Mxy^2+Ny^3$ with eight limit cycles in the neighborhood of the origin of coordinates.
Keywords and phrases:
Center-focus problem, Lienard systems of differential equations, cubic systems, limit cycles, Cherkas method.
Received: 12.12.2004
Citation:
Yu. L. Bondar, A. P. Sadovskii, “Variety of the center and limit cycles of a cubic system, which is reduced to lienard form”, Bul. Acad. Ştiinţe Repub. Mold. Mat., 2004, no. 3, 71–90
Linking options:
https://www.mathnet.ru/eng/basm180 https://www.mathnet.ru/eng/basm/y2004/i3/p71
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Abstract page: | 287 | Full-text PDF : | 116 | References: | 40 | First page: | 1 |
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