Optimal harvesting strategies of a stochastic competitive model with S-type distributed time delays and Lévy jumps

Abstract

Abstract The aim of this paper is to investigate the optimal harvesting strategies of a stochastic competitive Lotka–Volterra model with S-type distributed time delays and Lévy jumps by using ergodic method. Firstly, the sufficient conditions for extinction and stable in the time average of each species are established under some suitable assumptions. Secondly, under a technical assumption, the stability in distribution of this model is proved. Then the sufficient and necessary criteria for the existence of optimal harvesting policy are established under the condition that all species are persistent. Moreover, the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are given.

Keywords

• Optimal harvesting
• Competitive model
• White noise
• S-type distributed time delays
• Lévy jumps
• Stability in distribution