Role of competition in phytoplankton population for the occurrence and control of plankton bloom in the presence of environmental fluctuations

Termination of harmful algal blooms (HABs) and coexistence of phytoplankton–zooplankton populations are of great importance to human health, ecosystem, environment, tourism and fisheries. In this paper, we propose a three component model consisting of non-toxic phytoplankton (NTP), toxin producing phytoplankton (TPP) and zooplankton (Z). The growth of zooplankton species is assume to reduce due to toxic chemicals released by TPP population. We have extended the model proposed by Chattopadhyay et al. [Chattopadhyay, J., Sarkar, R.R., Pal, S., 2004. Mathematical modelling of harmful algal blooms supported by experimental findings. Ecol. Comp. 1, 225–235] by including competition terms between TPP and NTP. We observe the effect of competition factors both in the presence and absence of the environmental fluctuation. From our field as well as model analysis we observe that competition helps in the coexistence of the species, but if the effect of competition is very high on the TPP population, it results in planktonic bloom. It is shown that the coexistence equilibrium loses its stability when the competition coefficient crosses a critical value and resulting Hopf-bifurcation around the positive equilibrium depicting oscillations phenomena of the populations.