Exploring the Complexities of Predator Prey Interactions Effects of Fear Toxicants and Delayed Responses

Abstract

My research primarily aims to evaluate how different factors influence the dynamics of predator-prey interactions. These factors include the impact of fear on the birth and death rates of prey species, intraspecific competition among predator species, the carry-over effects of fear, gestation delays, and the influence of toxic substances. I analyze various dynamic properties, like extinction, persistence, equilibrium stability, local bifurcations etc. I delve into the complex interactions between predators and prey, where the fear induced by predators in prey species impacts not only their birth rates but also their death rates. Also, my analysis reveals that heightened levels of fear or increased intraspecific competition among predators can contribute to the survival of both populations, allowing them to coexist in a stable state. I have analyzed a predator-prey interaction model that explores the impact of predator-induced fear and its lingering carry-over effects, where the predator species has access to additional food sources. The findings denote that when the system reaches a interior equilibrium, an elevated level of fear can stabilize this state. Conversely, a stronger carry-over effect tends to induce oscillatory dynamics around the coexistence state. Thus, fear and its carry-over effects play contrasting roles in the stability of the coexistence equilibrium-while fear can promote stability, its carry-over effects can lead to instability and fluctuations in the system. Furthermore, these two predator-prey dynamics have been expanded to include the effects of toxicants, recognizing that the impact of toxic substances on ecological systems has recently emerged as a critical environmental concern. Again, the incorporation of a time delay, accounts for gestation periods, adds another layer of complexity to the dynamics of these systems, providing a more comprehensive understanding of their behavior. newline