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Nonlinear analysis in a nutrient-algae-zooplankton system with sinking of algae. (English) Zbl 1470.92236

Summary: A reaction-diffusion-advection model is proposed for the Zeya Reservoir to study interactions between algae and zooplankton, including the diffusive spread of algae and zooplankton and the sinking of algae. The model is investigated both with and without sinking. Conditions of Hopf and Turing bifurcation in the spatial domain are obtained, and conditions for differential-flow instability that gives rise to the formation of spatial patterns are derived. Using numerical simulation, the authors examine the impacts on algae of different nutrient concentrations, different sinking rates, and various diffusive spreading patterns. Finally, the models with and without sinking are compared, revealing that the sinking of algae plays an important role in the oscillations of algae and zooplankton. All these results may help to achieve a better understanding of the impact of algae in the Zeya Reservoir.

MSC:

92D25 Population dynamics (general)
35K40 Second-order parabolic systems
35K57 Reaction-diffusion equations
92D40 Ecology
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