Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL, Canada, A1C 5S7.
J Biol Dyn. 2012;6:148-65. doi: 10.1080/17513758.2010.544409. Epub 2011 Jun 24.
We present two simple plankton population models: one has instantaneous predation, another has delayed predation. The models consist of two coupled differential equations representing the interaction between phytoplankton and herbivorous zooplankton with additional effect of zooplankton predation by a constant fish population. We study the dynamical behaviour and investigate the conditions to guarantee the coexistence of two species, and address the stability and bifurcation under different density of fish, with or without the maturation time delay. Analytical methods and numerical simulations are used to obtain information about the qualitative behaviour of the models.
一个具有瞬时捕食，另一个具有延迟捕食。这些模型由两个耦合的微分方程组成，代表了浮游植物和草食性浮游动物之间的相互作用，以及浮游动物被恒定鱼类种群捕食的额外影响。我们研究了动力学行为，并研究了保证两种物种共存的条件，以及在不同鱼类密度下的稳定性和分岔，是否考虑成熟时间延迟。我们使用分析方法和数值模拟来获取有关模型定性行为的信息。
