Effects of Planktivorous Fish Community on a Two-Dimensional Plankton System with Allee Effect in Prey

Abstract

Embarking on a captivating journey of discovery, our research centers around unraveling the fascinating interaction between fish and plankton. Employing a predator–prey model, we delve into the dynamic interplay of Daphnia and Algae, while scrutinizing the profound influence of fish as a top predator. Our analyses suggest that in most situations, the plankton should show transitions in response to predation pressure by fish. Thus, there exist two distinct stable states, one in which Daphnia is controlled by fish and phytoplankton biomass is high and another in which Daphnia is relatively unaffected by planktivores and algae are controlled by Daphnia. Switches from one regime to the other occur abruptly at a critical fish density. Beyond deterministic exploration, we delve into the influence of the Allee parameter, which significantly increases the number of Daphnia in a free state. To investigate the complete global dynamics of the deterministic model, we present a two-parametric bifurcation diagram. We have also analyze all possible local and global bifurcations that the system could go through. We explore the corresponding stochastic system and investigate the critical transitions with the presence of environmental noise. To understand the probabilistic mechanism behind noise-induced outbreaks, we utilize advanced techniques such as stochastic sensitivity functions and the confidence domain method. These tools grant us unique insights into the captivating world of noise-induced transitions—where stochastic trajectories skillfully navigate from one stable equilibrium point to another.