Nutrient enrichment and phytoplankton toxicity influence a diversity of complex dynamics in a fear-induced plankton-fish model

In this paper, we contemplate the dynamics of an aquatic system consisting of three interacting species, phytoplankton, zooplankton, and fish. We assume that the evading risk of fish predation induces fear in zooplankton species, which affects its growth dynamics radically. On the other hand, zooplankton develop an anti-predator defense by taking temporary refuge. Interestingly, the system potentially exhibits multi stable configurations under identical ecological conditions by allowing different bifurcation scenarios, including multiple saddle-node and transcritical bifurcations with varying levels of nutrients, strength of phytoplankton toxicity, zooplankton refuge size and the cost of fear imposed by fish population. Further, by adding Gaussian white noise, we have extended the deterministic system to its stochastic version. We find that white noise appears to regulate the survival and extinction of model species. Comprehensive numerical simulations are consistent with mathematical results prognosticated by linear analysis. Overall, our study may provide a new insight into the mechanisms of emergence and mitigation of plankton blooms.