Modelling the impact of environmental pressure and fear effect on a plankton-fish ecosystem

Abstract This paper presents a mathematical prey-predator model to investigate the intricate, non-linear relationships between phytoplankton, zooplankton, and fish in a marine ecosystem. The model incorporates fundamental ecological processes, including logistic phytoplankton growth, zooplankton grazing on phytoplankton, and fish predation on zooplankton. Additionally, we consider the impact of extreme environmental pressures, including a fear effect, on the marine ecosystem. First, we examine the positivity and boundedness of the proposed model. Furthermore, all the equilibrium points are determined, and the local stability of the system is analyzed around each equilibrium point. The research also explores the impact of rising environmental pressure on population sizes among species. It concludes that greater environmental pressure could drive the system to extinction via a branch point bifurcation. Minimal environmental pressure will destabilize the system via a Hopf bifurcation. We also explore the impact of the fear cost on the zooplankton population and conclude that greater fear costs can cause system instability via another Hopf bifurcation. Theoretical calculations are confirmed by numerical simulations carried out using Mathematica and MATLAB software.