Optimal harvesting for a stochastic Lotka–Volterra predator-prey system with jumps and nonselective harvesting hypothesis

A stochastic Lotka–Volterra predator–prey system driven by both Brownian motion and Poisson counting measure is modeled and studied in this paper. A new ergodic method is proposed to solve the classical optimal harvesting problem. Equivalency between time averaged yield function and sustained yield function is proved by this new approach. The optimal harvesting strategy and the corresponding maximum yield with respect to stationary probability density are obtained. Several examples are taken to show that results in this paper are new even in the deterministic case. The method proposed in this paper can avoid trouble of solving the corresponding partial differential equations, and it can be extended to a more general high-dimensional case or some other stochastic system.