Expectation Of Sustainable Yield Research Articles

Global dynamics and optimal harvesting in a stochastic two-predators one-prey system with distributed delays and Lévy noise

ABSTRACT In this paper, we first investigate a stochastic two-predators one-prey model with Lévy noise and distributed delays. The global dynamical behaviour is discussed. The criteria on the existence of global positive solutions, stochastic boundedness, extinction and global asymptotic stability in the mean with probability one are established. And then, the harvesting for each species is introduced to the model. The optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY, for short) are further established.

Global dynamics in a stochastic three species food-chain model with harvesting and distributed delays

This paper proposes a stochastic three species food-chain model with harvesting and distributed delays. Some criteria for the global dynamics of all positive solutions, including the existence of global positive solutions, stochastic boundedness, extinction, global asymptotic stability in the mean, and the probability distribution, are established by using the stochastic integral inequalities, Lyapunov function method, and the inequality estimation technique. Furthermore, the effects of harvesting are discussed, the optimal harvesting strategy and the maximum of expectation of sustainable yield (MESY for short) are obtained. Finally, numerical examples are carried out to illustrate our main results.

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

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 of a competitive n-species stochastic model with delayed diffusions.

In this study, we propose an n-species stochastic model which considers the influences of the competitions and delayed diffusions among populations on dynamics of species. We then investigate the stochastic dynamics of the model, such as the persistence in mean of the species, and the asymptotic stability in distribution of the model. Then, by using the Hessian matrix and theory of optimal harvesting, we investigate the optimal harvesting problem, obtaining the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY). Finally, we numerically discuss some examples to illustrate our theoretical findings, and conclude our study by a brief discussion.

Optimal control strategy for an impulsive stochastic competition system with time delays and jumps

Driven by both white and jump noises, a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated. By using the comparison theorem of stochastic differential equations and limit superior theory, sufficient conditions for persistence in mean and extinction of two species are established. In addition, we obtain that the system is asymptotically stable in distribution by using ergodic method. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are derived from Hessian matrix method and optimal harvesting theory of differential equations. Finally, some numerical simulations are provided to illustrate the theoretical results.

Optimal harvesting control and dynamics of two-species stochastic model with delays

Taking the stochastic effects on growth rate and harvesting effort into account, we propose a stochastic delay model of species in two habitats. The main aim of this paper is to investigate optimal harvesting and dynamics of the stochastic delay model. By using the stochastic analysis theory and differential inequality technology, we firstly obtain sufficient conditions for persistence in the mean and extinction. Furthermore, the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY) are gained by using Hessian matrix, the ergodic method, and optimal harvesting theory of differential equations. To illustrate the performance of the theoretical results, we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients.