考虑病毒感染的营养浮游植物模型的复杂动力学性态分析
Complex Dynamics of a Nutrient-Phytoplankton Model with Disease
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摘要: 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. 得出了平衡点存在和局部稳定的条件, 利用Lyapunov函数方法讨论了某些边界平衡点的全局稳定性, 还通过数值模拟发现边界平衡点的双稳定现象、 Hopf分支现象, 以及正平衡点的Hopf分支现象, 该分支可以是超临界也可以是亚临界的.Abstract: In this paper, a model with one nutrient and two phytoplankton populations is proposed. Conditions for the existence and local stability of the equilibria are obtained. By means of Lyapunov function, the global stability of the boundary equilibria are obtained and some interesting numerical simulations are given by means of matlab, maple and matcont. Bistable phenomena are obtained at the boundary equilibrium. The existence of Hopf bifurcations around the boundary equilibrium and the interior equilibrium are discovered and these Hopf bifurcations can be supercritical or subcritical.
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