doi: 10.17706/ijapm.2025.15.1.1-12
Asymptotic Stability in a Controlled Stochastic Lotka-Volterra Model with Lévy Noise
Cutberto Romero-Meléndez
1,*
,
,
- 1 Basic Sciences Department, Metropolitan Autonomous University, Mexico.
- 2 Neurobiology Institute, National Autonomous University of Mexico, México.
- Manuscript received July 8, 2024
- revised September 20, 2024
- accepted October 17, 2024
- published January 17, 2025
Abstract
We consider a stochastic Lotka-Volterra model for one-predator-two- prey with driven by noise and Lévy jumps. The objective of the paper is to study this Lotka-Volterra model introducing controls on the deterministic part and on the Lévy noise, by means of Lyapunov approaches functions techniques. Assuming linear growth and Lipschitz conditions in the drift and diffusion terms, we prove the boundedness and the exponential stability of its solutions.
Keywords
- Lotka-Volterra model
- stochastic optimal control
- stability
- Lévy jumps
How to Cite
Cutberto Romero-Meléndez, David Castillo-Fernández, and Leopoldo González-Santos, "Asymptotic Stability in a Controlled Stochastic Lotka-Volterra Model with Lévy Noise," International Journal of Applied Physics and Mathematics, vol. 15, no. 1, pp. 1-12, 2025. https://doi.org/ 10.17706/ijapm.2025.15.1.1-12
Copyright & License
Copyright © 2025 by the authors. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).