On the dynamics of a class of Kolmogorov systems

Rachid Boukoucha

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 9 (2016) no. 1, pp. 11-16.

Résumé

In this paper we charaterize the integrability and the non-existence of limit cycles of Kolmogorov systems of the form \begin{equation*} \left\{ \begin{array}{l} x^{\prime }=x\left( P\left( x,y\right) +\sqrt{R\left( x,y\right) }\right) , \\ y^{\prime }=y\left( Q\left( x,y\right) +\sqrt{R\left( x,y\right) }\right) , \end{array} \right. \end{equation*} where $P\left( x,y\right) ,$ $Q\left( x,y\right) ,$ $R\left( x,y\right) ,$ homogeneous polynomials of degree $n,$ $n,$ $m,$ respectively.

Détail

Keywords: Kolmogorov system, first integral, periodic orbits, limit cycle.

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