Bifurcation Analysis of Stage-structured Prey-predator Interactions in Sea Turtle Populations

Abstract

In this study, a stage-structured prey-predator model is used to describe the dynamics of sea turtles and their marine predators across different life stages. Marine predators primarily target hatchlings, while mature sea turtles can survive independently and immature individuals often rely on external support. This paper employs stability analysis and bifurcation analysis and treating the conversion rate from sea turtle eggs to hatchlings as the bifurcation parameter. Graphical results, including bifurcation diagrams, phase-plane plots, and time series graphs, are produced with XPPAUT, Maple, and MATLAB, respectively. The analysis identifies a transcritical bifurcation point that marks a change in system stability under varying conversion rates. Moreover, the results demonstrate that the conversion rate strongly influences prey-predator dynamics: low rates can cause predator extinction, moderate rates allow coexistence, and high rates increase predation on hatchlings. Overall, the study highlights the ecological importance of hatching rates for maintaining balance and guiding conservation strategies, with particular attention to preventing species extinction.