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Integrability and non-existence of periodic orbits for a class of Kolmogorov systems

In: Tatra Mountains Mathematical Publications, vol. 81, no. 1
Sarbast Hussein - Tayeb Salhi - Bo Huang

Details:

Year, pages: 2022, 145 - 154
Language: eng
Keywords:
Kolmogorov differential systems, first integral, invariant algebraic curve, periodic orbit
Article type: Dynamical Systems
Document type: scientific paper pdf
About article:
In this article, we study the integrability and the non-existence of periodic orbits for the planar Kolmogorov differential systems of the form \begin{align*} \dot{x}=x\bl(Rn-1(x,y)+Pn(x,y)+Sn+1(x,y)\br), \dot{y}=y\bl(Rn-1(x,y)+Qn(x,y)+Sn+1(x,y)\br), \end{align*} where $n$ is a positive integer, $Rn-1$, $Pn$, $Qn$ and $Sn+1$ are homogeneous polynomials of degree $n-1$, $n$, $n$ and $n+1$, respectively. Applications of Kolmogorov systems can be found particularly in modeling population dynamics in biology and ecology.
How to cite:
ISO 690:
Hussein, S., Salhi, T., Huang, B. 2022. Integrability and non-existence of periodic orbits for a class of Kolmogorov systems. In Tatra Mountains Mathematical Publications, vol. 81, no.1, pp. 145-154. 1210-3195. DOI: https://doi.org/ 10.2478/tmmp-2022-0011

APA:
Hussein, S., Salhi, T., Huang, B. (2022). Integrability and non-existence of periodic orbits for a class of Kolmogorov systems. Tatra Mountains Mathematical Publications, 81(1), 145-154. 1210-3195. DOI: https://doi.org/ 10.2478/tmmp-2022-0011
About edition:
Publisher: Mathematical Institute, Slovak Academy of Sciences, Bratislava
Published: 22. 11. 2022
Rights:
https://creativecommons.org/licenses/by-nc-nd/4.0/