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Supersensitivity for a discrete-time aggregation model. (Spanish. English summary) Zbl 0941.92024

Summary: A discrete-time model from population biology is considered, which is the composition of a linear integral operator of dispersion with a nonlinear growth function. In a previous paper [ibid. 5, No. 1-2, 21-27 (1997; Zbl 0909.92024)], it was shown that such a model could generate metastable patterns of aggregation, and in the case of a unique region of aggregation, it was found that it occupied half the habitat, after an exponentially slow evolution.
This work introduces in the model certain exponentially small perturbations, whose dramatic effects are a noticeable modification for the speed of the frontier of aggregation, and an order one change in the final extent of the region of aggregation.

MSC:

92D25 Population dynamics (general)
39B99 Functional equations and inequalities

Citations:

Zbl 0909.92024
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