Optimal harvesting for a stochastic Lotka–Volterra predator‐prey system with jumps and nonselective harvesting hypothesis. (1st July 2015)

• Record Type: Journal Article
• Authors: Zou, Xiaoling; Wang, Ke
• Is Part Of: Optimal control applications and methods. Volume 37:Number 4(2016:Jul./Aug.)
• Page Start: 641
• Page End: 662
• Publication Date: 2015-07-01
• Subjects: white noise -- Poisson compensated random measure -- variation‐of‐constants formula -- asymptotic properties -- asymptotically stable in distribution; Control theory -- Periodicals; Mathematical optimization -- Periodicals; 629.8312
• DOI: 10.1002/oca.2185
• Languages: English
• ISSNs: 0143-2087

Abstract

Summary: 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. Copyright © 2015 John Wiley & Sons, Ltd.