Bifurcation Analysis of Predator-Prey Mathematical Model with Resource-Limited Growth and Predator Switching Behavior

Abstract

Ecology examines the interactions between organisms and their environment, with a particular focus on population dynamics, resource availability, and predator-prey relationships. This study presents a mathematical model designed to investigate the interactions between two prey populations, one in an unprotected region and the other in a protected region, along with a predator population and shared resource availability. The model employs nonlinear differential equations to capture processes such as prey growth, predation, and resource utilization. By identifying equilibrium points and conducting eigenvalue analysis, we assess the system’s stability. Numerical simulations demonstrate a range of outcomes, including stable states, cyclic behavior, and population collapse, depending on ecological conditions (parametric values). Biologically, predator-prey coexistence equilibria may lose stability, shifting to extinction or dominance scenarios. This makes bifurcation point. Bifurcation analysis reveals how competition and predation impact stability, with critical points marking transitions between coexistence, oscillations, or extinction. These results underscore the intricate balance of ecological forces and emphasize the significance of resource management and conservation in preserving ecosystem stability.