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Updated: Jul 2, 2026

Predicting the Effectiveness of Population Replacement Strategy Using Mathematical Modeling
Published on: July 4, 2007
Reduction of slow-fast discrete models coupling migration and demography
M Marvá1, E Sánchez, R Bravo de la Parra
1Dpto. Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain. marcos.marva@uah.es
Abstract:
This work deals with a general class of two-time scales discrete nonlinear dynamical systems which are susceptible of being studied by means of a reduced system that is obtained using the so-called aggregation of variables method. This reduction process is applied to several models of population dynamics driven by demographic and migratory processes which take place at two different time scales: slow and fast. An analysis of these models exchanging the role of the slow and fast dynamics is provided: when a Leslie type demography is faster than migrations, a multi-attractor scenario appears for the reduced dynamics; on the other hand, when the migratory process is faster than demography, the reduction process gives rise to new interpretations of well known discrete models, including some Allee effect scenarios.
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