Effects of Constant Nutrient Input and Dilution Rate of Nutrient in Plankton Community Ecosystem in Presence of Toxin

We present a complete parametric analysis of a nutrient–phytoplankton–zooplankton system influenced by toxin. In this paper, we have integrated Holling type II functional response in four-dimensional mathematical model. For this model, we investigate a qualitative analysis of the system in which studying the boundedness, existence and stability of non-negative equilibria. We perform different thresholds conditions to show the different dynamic behaviours of the system by using the model parameters. Our analysis leads to oscillatory behaviour of the system in which changing the dilution rate of nutrient and constant nutrient input. It is also observed that the fraction of the consumption of phytoplankton devoted to produce the inhibitor plays a key role to change the steady-state behaviour to oscillatory behaviour. Further, we see that higher values of toxin sensitivity of zooplankton concentration play a vital role to control this system. Finally, the numerical simulations to illustrate these analytical findings are presented.