Immigration and the persistence of chaos in population models

A simple population model is presented that exhibits both the period-doubling and the quasi-periodic routes to chaos with the variation of a single parameter. This fact is exploited to contrast the relative robustness of the two routes against structural perturbations in the form of added immigration terms. It is found that although sufficiently large levels of immigration eventually suppress chaotic dynamics in this model, chaos reached via the period-doubling route is much more easily inhibited than via the quasi-periodic one.