DOI: 10.14232/ejqtde.2026.1.55 ISSN: 1417-3875
Dynamic behaviour of a predator–prey model in a critical regime for predator with immigration in both species
Érika Diz-Pita, M. Victoria Otero-EspinarMost ecological interactions occur in open ecosystems, where species can enter or leave. Predator–prey dynamics are no exception. This work generalizes a predator–prey model by incorporating immigration for both species, making it more biologically relevant. We analyze a system with a Holling type II functional response in the positive quadrant of the Poincaré disk, the biologically meaningful region, including its behavior near infinity. We identify several realizable phase portrait configurations and provide sufficient conditions for the occurrence of a Hopf bifurcation giving rise to a small-amplitude limit cycle.