Research On Optimal Harvesting Of Two Types Of Stochastic Predator-prey Models

The harvesting of ecological system has always been a hot topic in the research of scholars.The maximum sustainable yield policy obtained through the study of the optimal harvesting of the system is an important ecological management tool to protect the survival of the population.This paper mainly studies the optimal harvesting problem of two kinds of stochastic predator-prey models.The optimal harvesting strategy and the optimal output function of two kinds of stochastic models are obtained by using two different harvesting functions.In the second chapter,we study the two dimensional Lotka-Volterra predator-prey model with variable harvesting function from invariant sets and the stability of invariant measures on invariant sets.First,the strong stochastic persistence and extinction of the population are obtained by the threshold analysis,and then the equivalence theorem is obtained by the ergodic property,so as to obtain the optimal harvesting strategies and the optimal output function.Finally,the persistence and extinction are illustrated by numerical examples.In the third chapter,“intermittent control” is used to model “summer fishing moratorium” phenomenon and a stochastic two-prey one-predator Lotka-Volterra model with intermittent harvesting is considered.In order to deal with intermittent harvesting in stochastic model,a new time averaged objective function is proposed.Besides,the corresponding optimal harvesting strategies are obtained by using the equivalent method(almost surely equivalency between time-averaged and expectation).An interesting result shows that intermittent harvesting can affect the optimal harvesting effort,but it cannot change the corresponding optimal output function yield.Finally,the results are illustrated by practical examples of marine fisheries and numerical simulations.Through the research in this paper,the optimal harvesting schemes of two types of Lotka-Volterra models are obtained,which providing a theoretical basic for the management of ecosystem harvesting problem.