On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems
For two-dimensional Kolmogorov system, where R ( x,y ), S ( x,y ), P ( x,y ), Q ( x,y ), M ( x,y ), N ( x,y ) are homogeneous polynomials of degrees m, a, n, n, b, b, respectively, we obtain an explicit expression of the first integral and prove the non-existence of periodic orbits and of limit cycles. We adduce an example of applicability of our result.