Reduction of slow-fast discrete models coupling migration and demography |
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Authors: | Marvá M Sánchez E Bravo de la Parra R Sanz L |
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Institution: | a Dpto. Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain b Dpto. Matemática Aplicada, E.T.S. Ingenieros Industriales, C. José Gutiérrez Abascal 2, 28006 Madrid, Spain c UR GEODES, IRD, 32, Avenue Henri Varagnat, 93143 Bondy Cedex, France |
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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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Keywords: | 39A11 92D25 |
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