【摘要】 营养和其消耗者之间的关系模型过去、现在和未来都是生态学和生态数学的重要内容之一.提出了一个一种营养,两种浮游植物并且其中一种浮游植物具有病毒感染的模型.并运用微分方程稳定性理论的相关知识和方法,对该模型的定性理论进行了研究.得出了模型平衡点存在和局部稳定的条件,同时在某些边界平衡点和正平衡点产生了Hopf分支,最后利用Lyapunov函数方法讨论了某些边界平衡点的全局稳定性.该模型的研究对我们进一步理解海洋生态系统的运行有一定的参考意义.更多还原

【Abstract】 The dynamic relationship between nutrient and their consumers has long been and will continue to be one of the dominant themes in both ecology and mathematical ecology system.Plankton are the basis of all aquatic food chain and phytoplankton in particular occupies the first trophic level.There are many models studying this area.A model with one nutrient and two phytoplankton populations is proposed in this paper.One of the phytoplankton population is divided into two classes: susceptible phytoplankton population and infected phytoplankton population which can consume nutrient but can not produce new individuals.Conditions for existence and local stability of the equilibria are obtained and Hopf bifurcations occur around the boundary equilibrium and the interior equilibrium with the help of differential equation stability theory.By means of Lyapunov function,the global stability of the rest boundary equilibria are obtained.The study of this model can offer some help to understand the loop of the ecology system.更多还原