Geodesic
On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 3-9.

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For two-dimensional Kolmogorov system, where $R\left( x,y\right)$, $S\left( x,y\right)$, $P\left( x,y\right)$, $Q\left( x,y\right)$, $M\left( x,y\right)$, and $N\left( x,y\right) $ are homogeneous polynomials of degrees $m$, $a$, $n$, $n$, $b$, and $b$, 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.
Keywords: Kolmogorov system, first integral, periodic orbits, limit cycle. 
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R. Boukoucha. On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2018), pp. 3-9. http://geodesic.mathdoc.fr/item/IVM_2018_1_a0/

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