Dynamics of a nutrient-plankton model with delay and toxicity

Abstract

In this paper, a dynamical system exploring the nutrient-plankton interaction has been studied to determine the impact of toxin liberation delay. It is well known that the toxins liberated by phytoplankton species are harmful to the growth and the life cycle of zooplankton species. Moreover, the process of toxin liberation is not immediate, but it follows some time delay. We have observed many significant features of the given model system like boundedness, positivity, Hopf-bifurcation and its direction, etc. From the analysis of this model, it is observed that the toxin liberation delay can include complexity in the system as time delay passes through its critical value. All analytical results are verified through numerical simulations, and some significant findings are interpreted from the ecological point of view.