Dynamical Analysis and Optimal Harvesting Strategy for a Stochastic Delayed Predator‐Prey Competitive System with Lévy Jumps

Abstract

This paper develops a theoretical framework to investigate optimal harvesting control for stochastic delay differential systems. We first propose a novel stochastic two-predator and one-prey competitive system subject to time delays and Lévy jumps. Then we obtain sufficient conditions for persistence in mean and extinction of three species by using the stochastic qualitative analysis method. Finally, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of delay differential equations. Moreover, some numerical simulations are given to illustrate the theoretical results.

Optimal Harvesting Strategies for Timber and Non-timber Forest Products with Nonlinear Harvesting Term

“…In 2016, Gaoue et al [9] developed a joint harvest model for timber and non-timber products based on a logistic timber growth equation with proportional harvest, which is the first continuous theoretical model for non-timber harvest (1 ) ,…”

“…Population dynamics is one of the branches of biomathematics, which focuses on the quantitative, spatial and structural dynamics of populations, and can be used to describe the dynamic relationships between populations and their environment and between populations and other populations, as well as to explain, predict, regulate and control the developmental processes and trends of species [1]. The updating and development of biological population dynamics models have effectively contributed to the human knowledge of biological systems.…”