IJPAM: Volume 103, No. 2 (2015)

ON THE NON-EXISTENCE OF LIMIT CYCLES
FOR A CUBIC KOLMOGOROV SYSTEMS

Rachid Boukoucha$^1$, Ahmed Bendjeddou$^2$
$^1$Department of Mathematics
Faculty of Sciences Exactes and Informatics
University of Jijel
18000 Jijel, ALGERIA
$^2$Departement de Mathematics
Faculty of Sciences
University of Setif
19000 Setif, ALGERIA


Abstract. In this paper we charaterize the integrability and the non-existence of limit cycles of cubic Kolmogorov systems of the form

\begin{displaymath}\left\{
\begin{array}{l}
x^{\prime }=x\left( \lambda +ax^{...
...=y\left( \mu +ux^{2}+vxy+wy^{2}\right)
\end{array}%
\right. ,\end{displaymath}

where $\lambda ,\mu ,a,b,c,u,v,w\in 
\mathbb{R}
$.

Received: April 7, 2015

AMS Subject Classification: 34C07, 37C27, 37K10

Key Words and Phrases: cubic Kolmogorov system, first integral, periodic orbits, limit cycle

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DOI: 10.12732/ijpam.v103i2.8 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 103
Issue: 2
Pages: 227 - 233


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