AGGREGATION METHODS IN DISCRETE MODELS

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Abstract
The aim of this work is to extend approximate aggregation methods for multi-time scale systems of ordinary differential equations to time discrete models. We give general methods in order to reduce a large scale time discrete model into an aggregated model for a few number of slow macro-variables. We study the case of linear systems. We demonstrate that the elements defining the asymptotic behaviours of the initial and aggregate models are similar to first order. We apply this method to the case of an agestructured population with sub-populations in each age classes associated to different spacial patches or different individual activities. A fast time scale is assumed for patch or activity dynamics with respect to aging and reproduction processes. Our method allows us to aggregate the system into a classical Leslie model in which the fecundity and aging parameters of the aggregated model are expressed in terms of the equilibrium proportions of individuals in the different activities or patches.

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