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Modeling fluctuations in a minimal plankton model: role of spatial heterogeneity and stochasticity. (English) Zbl 1198.92044
Summary: The present paper studies the naturally observed phenomenon of population fluctuation in the context of a minimal plankton model. The analysis of the basic model reveals asymptotic stable behavior that is unable to explain any kind of population outburst. We introduce the nonuniform spatial distribution of plankton by considering physical diffusion of the species concerned. The resulting reaction-diffusion equation model is first analyzed with constant diffusivity and then with variable diffusivity for the zooplankton. The model with variable diffusivity is analyzed by using Floquet theory. In both cases, the model is seen to exhibit stable behavior. Finally, we study another characteristic feature of any ecological population, namely, environmental fluctuations. We achieve this by perturbing the growth rate of phytoplankton and death rate of zooplankton by using colored noise. The resulting model is analyzed by evaluating the spectral density functions. It is observed that the stochastic model can generate a large fluctuation in population concentration for high amplitude driving forces.
MSC:
92D40Ecology
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