EXPLICIT FORM FOR THE FIRST INTEGRAL AND LIMIT CYCLES OF A CLASS OF PLANAR KOLMOGOROV SYSTEMS - Boukoucha, Rachid (Proceedings of the YSU A: Physical and Mathematical Sciences, 2021)
In this paper we characterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form equation* { arrayl x^′ =x( R( x,y) ( A( x,y) B( x,y) ) +P( x,y) ( C( x,y) D( x,y) ) ) , y^′ =y( R( x,y) ( A( x,y) B( x,y) ) +Q( x,y) ( V( x,y) W( x,y) ) ) , array . equation* where A( x,y), B( x,y), C( x,y), D( x,y), P( x,y), Q( x,y), R(x,y), V( x,y), W( x,y) are homogeneous polynomials of degree a, a, b, b, n, n, m, c, c, respectively. Concrete example exhibiting the applicability of our result is introduced.