Population dynamics of a two-stage migratory species with predation and capture

This paper provides a mathematical model for the evolution of a two-stage migratory species in an environment with predation and capture. Then, the qualitative dynamics of the model and its bifurcations are analyzed. In this sense, it is proved that the dynamics is determined by a threshold parameter RR. As a result, it is obtained that if R≥1R≥1, then the extinction equilibrium point is globally asymptotically stable, which assures that both species, prey and predators, are endangered. Finally, varying the parameters, different numerical simulations are produced from empirical data, showing different scenarios of the evolution of the populations which allow us to validate the model.