Research On Nutrient-Phytoplankton Model With Allelopathy

Based on the research of the water resources utilization and water ecological protection,this dissertation constructs several mathematical models which take allelopathic effect of phytoplankton into account in order to investigate the dynamic relationship between nutrient and phytoplankton.The allelopathic effect of phytoplankton on nutrient-phytoplankton is studied by using the qualitative and stable theory of differential equations.Periodic impulsive differential equation theory is applied to study the impact of the relationship between water resource and periodic releasing nutrient and the semi-continuous dynamical system theory is utilized to investigate the application of ecological water diversion in the prevention and control of water eutrophication.This paper is divided into four parts.In the first chapter,the background of water resources,plant allelopathy,water ecology protection,the mathematical research status of aquatic model and the related basic knowledge are introduced.In the second chapter,based on the inhibition of plant allelopathy on phytoplankton,a nutrient-phytoplankton model is systematically studied.On account of the theory of non-linear dynamic systems,the qualitative and stability analysis of the model are carried out.The conditions for the existence and stability of equilibrium and the absence of limit cycles are obtained.Moreover the bifurcation of the system is briefly discussed.In the third chapter,the effects of periodic impulsive releasing nutrient(fertilization)on fishery management are considered.A nutrient-phytoplankton model with periodic impulse control is constructed and studied by the application of Floquet theory and impulsive comparison theorem.The issue of threshold is explored.The sufficient conditions for the existence and global stability of periodic solutions with phytoplankton extinction and permanence of the underlying system are obtained.In the fourth chapter,in view of the research on the improvement of water environment by ecological water diversion,a mathematical model of nutrientphytoplankton which takes allelopathic effect of phytoplankton into consideration under state impulse feedback control is constructed.The successor function,the Bendixson domain theorem,the contraction mapping principle and stability criterion of semi-continuous dynamical system theory are applied to investigate the existence,uniqueness and stability of the order-1 periodic solution.