Exploring Dynamics of Predator-Prey Interactions: Fear, Toxicity, Carry Over and Environmental Fluctuations

Abstract

Predator-prey has a long background in the ecological environment. The activity of prey's daily life can be altered due to the presence of a predator. Also, some experimental studies have proved that the induced fear of predators felt by prey, has the capability to change both the birth and death rate of the prey species. The effect of such fear and its carry-over impact in a predator-prey model where predators get additional food has been analyzed in a toxic environment. This research delves into the complex dynamics of a predator-prey system within ecological contexts, highlighting the interactions between species and environmental effects. Key factors that are explored include fear effect, additional food for predators, and carry-over effects within a toxic environment. Additionally, the inclusion of a time delay factor accounts for gestation periods, further enriching the dynamic of the system. Environmental fluctuations are studied by incorporating Gaussian white noise into the system, allowing for an analysis of their impact. The study investigates how fear, carry-over effects, and environmental toxicity influence population dynamics. Notably, the delay parameter introduces a supercritical Hopf bifurcation, significantly enhancing the dynamics of the system. Moreover, environmental stochasticity adds complexity to such models by capturing fluctuations in population dynamics. Through bifurcation diagrams, valuable insights are gained about the behavior of the proposed system across various parameter values. This deeper understanding sheds light on the system's stability and response to various environmental influences.