| Abstract: |
| In this talk, we investigate the global dynamics of a Rosenzweig-MacArthur system incorporating an Allee effect in the prey population. Our analysis is carried out within the first quadrant of the Poincare disc, which provides a compactification of the phase space and enables a complete characterization of the system behavior at infinity. The Allee effect introduces a critical threshold below which the prey population cannot persist, thereby fundamentally altering the system bifurcation structure and long-term dynamics. We rigorously characterize equilibria, limit cycles, and their stability, and complement the theoretical results with numerical simulations that illustrate biologically relevant scenarios. Implications for ecological resilience and species extinction thresholds are also discussed. |
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