The Study Of Dynamic Behavior And Optimal Harvesting For Several Classes Of Prey-predator Models With Nondeterministic And Deterministic Parameters

As people's material and cultural needs are growing,human beings continue to expand the scope and range of exploitation and utilization in natural resources,which leads to the disruption of ecological balance such that the human living envi-ronment has been being seriously threatened.For example,land desertification,soil erosion,greenhouse effects and so on,are caused by human over-exploitation and over-utilization for natural resources.Some resource developers have been being plagued by the significant issue how to achieve maximization of economic benefit in exploitation of biological resources and keep sustainable development of popula-tion system,and this issue has received most attention from academia.According to biological background knowledge,many researchers have established the corre-sponding mathematical models,studied and analyzed the dynamical behaviors of models with the mathematical methods and computer simulations,and provided an effective theoretical reference for the developers.Based on this idea,the thesis studies the dynamical behaviors and optimal harvesting policy of three classes of prey-predator systems.The thesis consists of five chapters.The first chapter introduces the background and the research status of prey-predator models which are involved with ondeter-ministic parameters,delay,refuge,and harvesting factor and so on,and gives a brief introduction on the main work of this thesis.We close with some preliminaries.In the second chapter,by introducing interval number,we establish a prey-predator model with refuge and nondeterministic parameters,in which the harvest-ing for both the prey and the predator is considered.Firstly,we study the sufficient conditions for the existence and local stability of ecological equilibria for the model,and analyze its possible bionomic equilibria.Secondly,by applying the Pontryagin maximum principle we discuss the optimal harvest strategy,and obtain the optimal equilibrium and the optimal harvest effort.Finally,we verify our theoretical results by numerical simulations.The third chapter establishes a prey-predator model with discrete delay or noise,and only consider harvesting for the predator.Firstly,we consider digest delay and harvesting,establish delay differential function,and apply the stability theory and Hopf bifurcation theory of delay differential equation achieve to the conditions for local stability of the positive equilibrium and Hopf bifurcation.Furthermore,by the center manifold and normal form theory we discuss the stability and direction of Hopf bifurcation.Secondly,considering the effect of white noise that the growth of the prey and the natural mortality of the predator in a stochastic environment,we discuss the fluctuation intensity of the stochastic system.On the other hand,considering the effect of the standard Gaussian white noise rather than delay,we transform the stochastic model into Ito stochastic differential equation by the s-tochastic averaging method.Calculating the Lyapunov exponent and the extreme values of invariant measure,we obtain the local stochastic stability and stochastic Hopf bifurcation of the model.Finally,without the impacts of delay and white noise we discuss the optimal harvesting strategy and the optimal equilibrium of the model and the optimal harvesting effort by using Pontryagin's maximum principle.In the fourth chapter,motivated by a class of prey-predator model with con-tinuous distribution delay,we consider respectively three situations,i.e.,harvesting for both the prey and the predator,harvesting for the prey and harvesting for the predator,to establish three eco-economic models which incorporates into taxation control.Applying the method of chain transformaiton,the three continuous distri-bution delay differential model ar translated into the corresponding models without delays,then we discuss respectively the existence of the equilibria of these models without delays,and obtain sufficient conditions for the local asymptotic stability of the equilibria by Routh-Hurwitz criterion.We also study the optimal harvesting strategies of the models,namely,the expressions of optimal taxation.Finally,we verify our theoretical results by numerical simulations.Chapter 5 summarizes the main contents of the thesis,and makes a prospect for the future research work.