Research On Stochastic Properties And Harvest Problems For Several Kinds Of Population Models

Considering the effects of environmental disturbance on the growth of population and the effects of changing price and cost on the harvest of population,three kinds of stochastic population models and one bioeconomic model are established.For these stochastic population models,the oscillation control problem,the critical conditions of persistence and extinction for population,and the influence of noise on the stationary probability distribution function are mainly analyzed.And for the bioeconomic model,the dynamic behavior is mainly analyzed.The contents of this paper are arranged as follows:In Chapter 1,we briefly introduce the relevant background,researchful significance and researchful developments of stochastic population models and the bioeconomic model.In Chapter 2,we study a stochastic phytoplankton-zooplankton model.The ensemble mean response of the model is derived by the orthogonal polynomial approximation method.The os-cillation control problem is discussed through numerical simulation.It is found that the periodic oscillation of the phytoplankton-zooplankton model can be controlled by the catchability coeffi-cients,and the control efficiency of the stochastic model is superior to that of the deterministic model.In Chapter 3,we study a stochastic single population model with Allee effect.The critical conditions of persistence and extinction for the population are obtained:whenσ~2≥2(r-a),the zero solution of the stochastic model is stable,which implies the population tends to be extinct;whenσ~2<2(r-a),the stochastic model has a unique positive stationary probability distribution,which implies the population can continue to survive.It is found that environmental disturbance is not conducive to the sustainable survival of the population.In Chapter 4,we study a stochastic single population model with multiplicative and addi-tive bounded noises.The corresponding approximate Fokker-Planck equation is derived by using Novikov theorem,and then the stationary probability distribution function is obtained.The in-fluence of the relevant parameters of noise on the extreme points of the stationary probability distribution function is discussed through numerical calculation.It is found that in the case of positive correlation and negative correlation,the effects of noise parameters on the extreme points are opposite,and the effects on the distance between the extrem points are also opposite.In Chapter 5,we study a population model with Allee effect and harvest under dynamic price.The dynamic properties of this model are analyzed,including the stability of equilibrium points and the existence of Hopf bifurcation.And the main results are explained from the perspective of bioeconomics.In Chapter 6,we give the conclusion of this paper.