Modeling and Analysis of a Marine Plankton System with Nutrient Recycling and Diffusion

This article describes a nutrient-phytoplankton-zooplankton system with nutrient recycling in the presence of toxicity. We have studied the dynamical behavior of the system with delayed nutrient recycling in the first part of the article. Uniform persistent of the system is examined. In the second part of the article, we have incorporated diffusion of the plankton population to the system and dynamical behavior of the system is analyzed with instantaneous nutrient recycling. The condition of the diffusion driven instability is obtained. The conditions for the occurrence of Hopf and Turing bifurcation critical line in a spatial domain are derived. Variation of the system with small periodicity of diffusive coefficient has been studied. Stability condition of the plankton system subject to the periodic diffusion coefficient of the zooplankton is derived. It is observed that nutrient-phytoplankton-zooplankton interactions are very complex and situation specific. Moreover, we have obtained different exciting results, ranging from stable situation to cyclic oscillatory behavior may occur under different favorable conditions, which may give some insights for predictive management. (C) 2014 Wiley Periodicals, Inc.