Effects of toxicants on Phytoplankton-Zooplankton-Fish dynamics and harvesting

In this paper, a three species predator-prey interaction model among Phytoplankton, Zooplankton and Fish has been developed in the presence of toxicant. It is assumed that Phytoplankton grows logistically and its growth rate is affected by toxin release in the environment through different natural and human activities. It is considered that Zooplankton consumes only Phytoplankton. Fish consumes both Phytoplankton as well as Zooplankton. Here, it is also assume that Phytoplankton releases some toxin in the environment which makes some death on Zooplankton. Also, it is considered that toxicant in the environment are increased constantly for different natural and human behavior. Then, different equilibrium points have been determined and the stability of the proposed system has been analyzed around these equilibrium points. Hopf bifurcation analysis has been done with respect to the contact rate between Phytoplankton and Environmental toxin (γ), constant rate of increase of Environmental toxin (A) , depletion rate of environmental toxin (d1), harvesting effort (E) and rate of releasing toxin by Phytoplankton (ρ). From this study, it is seen that these parameters have a big role on the stability of this predator prey system. Finally, some numerical simulation results have been shown to verify our analytical findings.