A class of Kolmogorov differential system is introduced, we show that under suitable assumptions, one, two or four algebraic limit cycles can occur, these limit cycles are analytically given.

A class of Kolmogorov differential system is introduced.We show that under suitable assumptions on parameters, an algebraic hyprbolic limit cycle can occur, the explicit expression of this limit cycle is given.

No abstract

For a given algebraic curve, we exhibit Kolmogorov dierential systems, and we show that these systems admit precisely the bounded components of the curve as hyperbolic limit cycles if certain conditions on the parameters of the system are satised.

A class of Kolmogorov differential system is introduced. It is shown that under suitable assumptions on degrees and parameters, algebraic limit cycles can occur. we propose an easy algorithm to test the existence of limit cycles and we give them explicit expressions.