Interspecies competition between phytoplankton and zooplankton in marine ecosystem

Abstract

In this paper, we propose and analyze a plankton system consisting of two plankton species one is toxin producing plankton, another is non-toxin producing plankton and zooplankton population which depends on both the phytoplankton species. We investigate the boundedness and stability criteria of the system and existence conditions of all possible equilibria. It is observed that if the inhibitory effects of the toxin producing phytoplankton crosses a certain critical value, the system enters into Hopf bifurcation. It is observed that the carrying capacity of non toxin phytoplankton population plays an important role to change steady state to oscillatory behavior of the system. Further, we have studied a path of optimal harvesting policy by introducing the Pontryagin’s maximum principle. Computer simulations illustrate the results.