The Several Dynamical Researches On Population Ecology System

Population ecology is an important branch of Mathematical Biology.It has been paid more and more attention by a large number of scholarsincluding home and abroad due to its wide authenticity and tremendouspracticability. This paper mainly discusses the spatiotemporal complexinfluence of Allee effect and delay effect in population ecology system.In Chapter1, the research background and research situation of thepopulation ecology system are in brief introduced. In addition, some basicconcepts and theorems are also presented, which are theoretical basis andfrequently used in following chapters.In Chapter2, spatiotemporal dynamics in a diffusive populationecology system with double Allee effect are studied. Based on theMathematics and biological significance, a phytoplankton-zooplanktonpredator-prey system with double Allee effect is established. According tothe linear stability analysis in a reaction-diffusion equation, the stabilityof constant equilibria of system and the condition of global stability of theunique interior equilibrium are obtained. What’s more, boundedness ofthe solutions and the condition as well as property of the Hopf bifurcationand steady state bifurcation are also studied. The time evolution andsolution of system are plotted by simulations in the end.In Chapter3, the dynamical behavior of a population ecologysystem with delay effect are discussed. Based on an already existingnutrient-plankton model, a biological system with delay effect isestablished. With Mathematical analysis, the conditions which equilibria and Hopf bifurcation exist are obtained. According to the center manifoldtheory, the direction of Hopf bifurcation and the stability of periodicsolutions are also discussed. Morever, numerical results verified thetheoretical results.In Chapter4, the influence of double delays effect are studied. Thestability of equilibria and the condition when Hopf bifurcation occurs arediscussed. What’s more, the condition of global stability of the interiorequilibrium is obtained with the upper-lower solution method. Numericalsimulation are showed in the end.