The impact of additional food on plankton dynamics in the absence and presence of toxicity

Abstract

This article represents a three-dimensional dynamical system which studies the impact of additional food on the plankton system in the absence and presence of toxicity. It is determined that available additional food and toxin produced by phytoplankton play a crucial role in the termination of harmful algal blooms. The significance of the parameter, additional food, lies in the fact that its limited availability can terminate planktonic blooms when the concentration of toxicity is high. The positivity, boundedness, and permanence of the system are proved to make the model biologically valid. The existence of different biological feasible equilibria and their local stability criteria are determined analytically under certain conditions. The Hopf-bifurcation analysis is carried out by considering additional food as a bifurcation parameter. All the theoretical results are verified numerically. Our results indicate that the prey and predator population are never extinct and survive at a stable level when the additional food is available for the predator population.