Non-algebraic limit cycles for some planar polynomial systems (original) (raw)

Abstract

We determine conditions for planar systems of the form dx dt=-x 3 +2(1+3λ)yx 2 -2xy 2 +(1+4λ)y 3 +x(ax 4 +bx 2 y 2 +cy 4 ),dy dt=-2(1+4λ)x 3 -yx 2 -(6λ+1)xy 2 -2y 3 +y(ax 4 +bx 2 y 2 +cy 4 ), where a,b,c and λ are real constants, to possess non-algebraic limit cycles. This is done as an application of some theorems providing the existence of non-algebraic limit cycles of the family of systems: dx dt=P n (x,y)+xR n (x,y),dy dt=Q n (x,y)+yR n (x,y), where P n (x,y),Q n (x,y) and R n (x,y) are homogeneous polynomials of degree n. The tool for proving our result is based on methods developed by Khalil I. T. Al-Dosary [Int. J. Math. 18, No. 2, 179–189 (2007; Zbl 1121.34036)] and A. Gasull, H. Giacomini and J. Torregrosa [J. Comput. Appl. Math. 200, No. 1, 448–457 (2007; Zbl 1171.34021)].

bendjeddou ahmed hasn't uploaded this paper.

Let bendjeddou know you want this paper to be uploaded.

Ask for this paper to be uploaded.