Reduction of slow-fast discrete models coupling migration and demography.
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.
Marvá
M
M
Dpto. Matemáticas, Universidad de Alcalá, 28871 Alcalá de Henares, Spain. marcos.marva@uah.es
Sánchez
E
E
Bravo de la Parra
R
R
Sanz
L
L
D025041:Animal Migration; D000818:Animals; D003710:Demography; D004463:Ecology; D008954:Models, Biological; D015233:Models, Statistical; D011157:Population Dynamics; D013997:Time Factors