Modelling of phytoplankton allelopathy with Monod–Haldane-type functional response—A mathematical study

In this paper, a three-tier model of phytoplankton, zooplankton and nutrient is considered and stability of different equilibrium points is analyzed along with Hopf-bifurcation around coexisting equilibrium point. Here, we have assumed toxication process as the guiding factor for bloom formation as well as its termination and this process is incorporated into our model by choosing the zooplankton grazing function as a Monod–Haldane function due to the phytoplankton toxicity. Extensive numerical simulations have been performed to validate the analytical findings and these simulation work reveal the chaotic oscillation exhibited by the model system for certain choice of the parameter values.