Impact of refuge phytoplankton: A bottom-up top-down plankton-fish interaction model

Abstract

This study investigates the impact of phytoplankton refuges on the stability of the plankton-fish ecosystem.
Through the analysis of various equilibria's coexistence and stability conditions, we observe that once the strength of phytoplankton refuges surpasses a critical threshold, the coexistence equilibrium becomes unstable and undergoes Hopf bifurcation, leading to oscillations in all species. The direction of the Hopf bifurcation and global stability are also determined. Additionally, the study shows that bottom-up and top-down effects such as the intrinsic growth rate of phytoplankton, mortality rate, and conversion rate of fish population play significant roles in facilitating transitions between different steady states, particularly concerning transcritical bifurcation.
Lastly, we perform numerical simulations to validate the analytical findings. Our findings have important implications for understanding the complex dynamics of plankton-fish ecosystems and highlight the crucial role of phytoplankton refuges in shaping these dynamics.