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Effects of immigration on the dynamics of simple population models. (English) Zbl 0949.92023
Summary: Many simple population models exhibit the period doubling route to chaos as a single parameter, commonly the growth rate, is increased. Here we examine the effect of an immigration process on such models and explain why in the case of one-dimensional (“single-humped”) maps, immigration often tends to suppress chaos and stabilise equilibrium behaviour or cyclical oscillations of long period. The conditions for which an increase of immigration “simplifies” population dynamics are examined.

MSC:
92D25 Population dynamics (general)
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