Optimal Harvesting of a Stochastic Lotka-Volterra Competition Model with Periodic Coefficients

TL;DR

This paper develops a framework for optimal harvesting in a stochastic Lotka-Volterra competition model with periodic coefficients, providing conditions for species persistence, extinction, and explicit optimal harvesting strategies.

Contribution

It introduces new conditions for species persistence and extinction, and derives explicit formulas for optimal harvesting efforts in a stochastic, periodically varying environment.

Findings

Existence of positive periodic solutions under certain conditions

Conditions for species persistence and extinction in the model

Explicit expressions for optimal harvesting effort and maximum sustainable yield

Abstract

This paper systematically investigates the optimal harvesting of a stochastic Lotka-Volterra competition model with periodic coefficients. Sufficient conditions for the extinction and persistence in the time average of each species are established. Using Khasminskii's stability theory with suitable Lyapunov functions, we establish sufficient conditions to guarantee the existence of positive periodic solutions to the model. Under certain assumptions, the stability in distribution of this model is proved. Then, we obtain the existence of an optimal harvesting policy and provide explicit expressions for the optimal harvesting effort and the maximum sustainable yield. Finally, we demonstrate our key findings numerically using the Euler-Maruyama method implemented in Python.