Delay Dynamics Problems Researches Of Several Kinds Of Hydro-plankton Model

The problems of eutrophication have received extensive attention in recent years,in particular,red tide,algal bloom caused by eutrophication.By means of the theory of delay differential equations and the relevant theory of aquatic ecology,this paper discussed the timed delay dynamics problems of several kinds of hydro-plankton model.Firstly,a kind of nutrition-aquatic phytoplankton ecomodel was constructed,and the delay dynamics problems were studied.In theoretical work,the persistent of model and the existence and stability of positive equilibrium were analyzed,and derived the critical conditions for the occurrence of Hopf branch in the model.The simulation work verified the feasibility of theoretical analysis,and the sensitivity analysis of the model was given.Then,on the basis of the nutrition-aquatic phytoplankton ecomodel that presented in Chapter II,distribute delay that exist in nutrient equation was replaced with discrete delay,and analyzed the stability of positive equilibrium of model under double time delays,and studied the relevant problems of Hopf branch.Meanwhile,we discussed the dynamic behaviors of model under six different conditions,and the results showed that double time delays plays a key role in equilibrium state transition of model.Finally,a kind of dissolved oxygen-aquatic phytoplanktonzooplankton ecomodel with a Holling-type II functional response was constructed,and qualitative and numerical study of its delay dynamics problems were processed.The existence and local asymptotic stability of equilibrium of model were analyzed,and derived the critical conditions for the existence of Hopf branch in the model and studied the relevant problems of Hopf branch.The simulation proofed the threshold condition for the occurrence of Hopf branch,and verified the feasibility and veracity of theoretical analysis.