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

Cite: Cutberto Romero-Meléndez, David Castillo-Fernández, 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.

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