The dynamics of two harmful phytoplankton and herbivorous zooplankton system

In this paper, a mathematical model consisting of the two harmful phytoplankton interacting with a herbivorous zooplankton is proposed and studied. The existence of all possible equilibrium points is carried out. The dynamical behaviors of the model system around biologically feasible equilibrium points are studied. Suitable Lyapunov functions are used to construct the basins of attractions of those points. Conditions for which the proposed model persists are established.The occurrence of local bifurcation and a Hopf bifurcation are investigated. Finally, to confirm our obtained analytical results and specify the vital parameters, numerical simulations are used for a hypothetical set of parameter values