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Deterministic and stochastic analysis of a delayed allelopathic phytoplankton model within fluctuating environment. (English) Zbl 1218.34098

Summary: We consider a two-dimensional model for two competitive phytoplankton species where one species is toxic phytoplankton and other is a non-toxic species. The logistic growth of both the species follows the Hutchinson type growth law. First, we briefly discuss basic dynamical properties of non-delayed and delayed model systems within deterministic environment. Next, we formulate the stochastic delay differential equation model system to study the effect of environmental driving forces on the dynamical behavior. We calculate the population fluctuation intensity (variance) for both species by the Fourier transform method. Numerical simulations are carried out to substantiate the analytical findings. Significant results of our analytical findings and their interpretations from ecological point of view are provided in the concluding section.

MSC:

34K60 Qualitative investigation and simulation of models involving functional-differential equations
34K18 Bifurcation theory of functional-differential equations
92D25 Population dynamics (general)
34K20 Stability theory of functional-differential equations
34K50 Stochastic functional-differential equations
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