ISSN:
1572-8358
Keywords:
Approximate aggregation of variables
;
population dynamics
;
perturbations
;
time scales
;
eigenvalues and eigenvectors analysis
Source:
Springer Online Journal Archives 1860-2000
Topics:
Biology
Notes:
Abstract Aggregation of variables allows to approximate a large scale dynamical system (the micro-system) involving many variables into a reduced system (the macro-system) described by a few number of global variables. Approximate aggregation can be performed when different time scales are involved in the dynamics of the micro-system. Perturbation methods enable to approximate the large micro-system by a macro-system going on at a slow time scale. Aggregation has been performed for systems of ordinary differential equations in which time is a continuous variable. In this contribution, we extend aggregation methods to time-discrete models of population dynamics. Time discrete micro-models with two time scales are presented. We use perturbation methods to obtain a slow macro-model. The asymptotic behaviours of the micro and macro-systems are characterized by the main eigenvalues and the associated eigenvectors. We compare the asymptotic behaviours of both systems which are shown to be similar to a certain order.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00713565
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