Investigation of the properties of spatially homogeneous mathematical model of the four-component plankton system

The paper presents analytical and numerical study of the dynamic behavior of a spatially homogeneous mathematical model of the four-component plankton system. The model includes nutrients, phytoplankton, zooplankton and plankton detritus. It was considered the most important properties of the model based on changes in the order of the enzymatic reaction, which describes the nonlinear process of decomposition of detritus, as well as the rate of release of metabolites of phytoplankton cells. It was studied two versions of the model. In the first, simpler case, it was assumed that zooplankton can consume only phytoplankton. The second version of the model takes into account the fact that zooplankton are food preferences in food, and he can eat and phytoplankton and detritus. Both models take into account the most important processes that determine the temporal dynamics of nutrients, phytoplankton, zooplankton and detritus in aquatic ecosystems. As a result of computational experiments it was shown that changes in the rate of release of metabolites by cells of phytoplankton, the order of the enzymatic reaction and food preferences of zooplankton leads to quite definite and regular changes of phase portraits of the model system. It was established that there are ranges of parameters for which exist a high sensitivity of plankton system to external influences and internal fluctuations of the components of the model.