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

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IVM_2018_1_a0,
     author = {R. Boukoucha},
     title = {On the non-existence of periodic orbits for a class of two-dimensional {Kolmogorov} systems},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {3--9},
     publisher = {mathdoc},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2018_1_a0/}
}
TY  - JOUR
AU  - R. Boukoucha
TI  - On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2018
SP  - 3
EP  - 9
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2018_1_a0/
LA  - ru
ID  - IVM_2018_1_a0
ER  - 
%0 Journal Article
%A R. Boukoucha
%T On the non-existence of periodic orbits for a class of two-dimensional Kolmogorov systems
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2018
%P 3-9
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2018_1_a0/
%G ru
%F IVM_2018_1_a0
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/