Dynamical study of nutrient-phytoplankton model with toxicity: Effect of diffusion and time delay

A harmful algal bloom is one of the significant concerns of marine biodiversity. The control of such algal bloom is required for the conservation of marine ecology. The proposed work discusses a model for interacting nutrient phytoplankton systems with the effect of toxic chemicals released by phytoplankton and time delay in toxin liberation. Our main aim is to provide a great insight into the impact of toxins and time delay on the dynamics of nutrient-phytoplankton. We investigate the stability of system dynamics, and the condition for the existence of Turing instability is obtained. The role of time delay is also investigated for the proposed system. The numerical simulation shows that toxin release rate, the diffusion coefficient of nutrients, and time delay significantly impact system dynamics. We observe that increasing values of toxin release results in the system dynamics show stable and oscillatory behavior without diffusion. The spatial and spatio-temporal patterns show that the higher value of the rate of toxin release lead to periodic and standing waves. Finally, we observe that the time delay in toxin distribution term stabilizes and destabilizes the system dynamics.