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where x(t) and y(t) represent the population density of two species at time t, and F (x, y) , G(x, y) are the capita growth rate of each specie, usually, such systems are called Kolmogorov systems. Kolmogorov models are widely used in ecology to describe the interaction between two populations, and a limit cycle corresponds to an equilibrium state of the system. When F (x, y) and G(x, y) are polynomials of degrees > 2, limit cycles can occur and there is an extensive literature dealing with their existence, number and stability (see for instance May [13], Lloyd, Pearson,Saèz and Szántó [11, 12], Huang [8], Huang, Wang, Cheng [9], Huang, Zhu [10], Boqian and Demeng [4], Cheng [5], and references therein), but to our knowledge, the

Kolmogorov System with Explicit Hyperbolic Limit Cycle