On the non existence of periodic orbits for a class of two dimensional Kolmogorov systems
Authors: Rachid Boukoucha
Journal: e-Journal of Analysis and Applied Mathematics (e-JAAM), e-ISSN 2544-9990
Volume: 2021 · Pages: 1 - 11
Published Online: 22 Nov 2021
Abstract: In this paper we characterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form x=x(B1(x,y), | A3(x,y)A4(x,y)| + B3(x,y)| A1(x,y)A2(x,y)| ), y=y(B2(x,y)| A5(x,y)A6(x,y)| + B3(x,y)| A1(x,y)A2(x,y)| ) where A1( x,y) , A2( x,y) , A3( x,y) , A4( x,y) , A5( x,y) , A6( x,y) , B1( x,y) , B2( x,y), B3( x,y) are homogeneous polynomials of degree a, a, b, b, c, c, n, n, m respectively. Concrete example exhibiting the applicability of our result is introduced.
Keywords: Kolmogorov system, first integral, periodic orbits, limit cycle