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  4. A Levy process approach coupled to the stochastic Leslie–Gower model

A Levy process approach coupled to the stochastic Leslie–Gower model

MMC.
2024;
Volume 11, Number 1
: pp. 178–188
https://doi.org/10.23939/mmc2024.01.178
Received: June 26, 2023
Revised: January 25, 2024
Accepted: February 19, 2024

Ben Said M., Aghoutane N., Azrar L. A Lévy process approach coupled to the stochastic Leslie–Gower model.  Mathematical Modeling and Computing. Vol. 11, No. 1, pp. 178–188 (2024)

Authors:
  1. M. Ben Said
  2. N. Aghoutane
  3. L. Azrar
1
MMA, FPL, Abdelmalek Essaadi University
2
Mathematical Modeling and Scientific Computing (M2CS), Department of Applied Mathematics and Informatics, ENSIAS, Mohammed V University in Rabat
3
Research Center ST2I, M2CS, Department of Applied Mathematics and Informatics, ENSAM, Mohammed V University in Rabat

This paper focuses on a two-dimensional Leslie–Grower continuous-time stochastic predator–prey system with Lévy jumps.  Firstly, we prove that there exists a unique positive solution of the system with a positive initial value.  Then, we establish sufficient conditions for the mean stability and extinction of the considered system.  Numerical algorithms of higher order are elaborated.  The obtained results show that Lévy jumps significantly change the properties of population systems.

Leslie–Gower
SDEs
Itô's formula
extinction
stochastic predator–prey model
Taylor method
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