On the dynamics of a class of Kolmogorov systems

摘要

In this paper we charaterize the integrability and the nonexistenceof limit cycles of Kolmogorov systems of the form???????x′= x(P (x; y) +(R(x;y)S(x;y)) );y′= y(Q(x; y) +(R(x;y)S(x;y)) );where P (x; y) ; Q(x; y) ; R(x; y) ; S (x; y) are homogeneous polynomialsof degree n; n; m; a respectively and 2 Q?. Concrete example exhibitingthe applicability of our result is introduced.