Dynamical Analysis And Control In Two Kinds Of Bio-economic Systems With Two Delays

Biological population dynamics is one of the main research contents of biodynamics.The relationship between populations includes prey-predator relationship,reciprocal relationship,and competitive relationship.In the living environment of biological populations,some stochastic factors can not be avoided,which will affect the populations.The biological population systems can be divided into deterministic systems and stochastic systems according to whether stochastic factors are considered.Some of the behaviors in the population are time-delayed,with the introduction of time delays,a biological population model can better reflect the relationship between populations.On the other hand,with the demand of people for economic interests,commercial capture is considered and established an economic interest equation in system.The content of this thesis is mainly divided into four sections.Firstly,the research status of biological population dynamics and some basic concepts related to this research are introduced,and some basic knowledge to be used is introduced.Secondly,the predator-predator fishery model was studied,which considered the gestation time delay of the prey and the pregnancy time delay of predator,the prey and predator were captured commercially and the economic interests equation were established;Positivity and uniform persistence of solutions are studied;Stability of the proposed system with different combinations of time delays is studied.Finally,the optimal capture strategy for predatorpredator fishery model with double time delay is discussed.Thirdly,a double time-delayed hybrid plankton economic model with stochastic fluctuations is established,which not only considers the existence of time delay in the system and commercial capture of the population,but also introduces Gaussian white noise into the proposed system to describe the stochastic factors of system.For deterministic system without double time delays,existence of singularity induced bifurcation is studied due to variation of economic interest of commercial harvesting,and state feedback controllers are designed to eliminate singularity induced bifurcation.For deterministic system with double time delays,positivity and uniform persistence of solutions are studied,and some sufficient conditions associated with asymptotic stability of interior equilibrium are investigated.For stochastic system without double time delays,stochastic stability is discussed based on singular boundary theory of diffusion process.For stochastic system with double time delays,existence and uniqueness of global positive solution are investigated,and asymptotic behaviors of the interior equilibrium are studied by constructing appropriate Lyapunov functions.Finally,some conclusions are carried out and author puts forward the innovations and unsolved problems of this thesis.