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IMCS/Publications/BASM/Issues/BASM n.3 (46), 2004/

Variety of the center and limit cycles of a cubic system, which is reduced to Lienard form. (English)

Authors: Y.L. Bondar, A.P. Sadovskii

Abstract

In the present work for the system x' = y(1+Dx+Px2), y' = -x + Ax2 + 3Bxy + Cy2 + Kx3 + 3Lx2y + Mxy2 + Ny3 25 cases are given when the point O(0,0) is a center. We also consider a system of the form x' = yP0(x), y' = -x + P2(x)y2 + P3(x)y3, for which 35 cases of a center are shown. We prove the existence of systems of the form x' = y(1+Dx+Px2), . = -x + lambda y + Ax2 + Cy2 + Kx3 + 3Lx2y + Mxy2 + Ny3 with eight limit cycles in the neighborhood of the origin of coordinates.

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