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

Rok, strany: 2022, 145 - 154

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(R_n-1(x,y)+P_n(x,y)+S_n+1(x,y)\br), \dot{y}=y\bl(R_n-1(x,y)+Q_n(x,y)+S_n+1(x,y)\br), \end{align*} where $n$ is a positive integer, $R_n-1$, $P_n$, $Q_n$ and $S_n+1$ 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.

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

Vydavateľ: Mathematical Institute, Slovak Academy of Sciences, Bratislava

https://creativecommons.org/licenses/by-nc-nd/4.0/