David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Acta Biotheoretica 46 (3):273-297 (1998)
In this work we extend approximate aggregation methods in time discrete linear models to the case of time varying environments. Approximate aggregation consists in describing some features of the dynamics of a general system involving many coupled variables in terms of the dynamics of a reduced system with a few number of variables. We present a time discrete time varying model in which we distinguish two time scales. By using perturbation methods we transform the system to make the global variables appear and build up the aggregated system. The asymptotic relationships between the general and aggregated systems are explored in the cases of a cyclically varying environment and a changing environment in process of stabilization. We show that under quite general conditions the knowledge of the behavior of the aggregated system characterizes that of the general system. The general method is also applied to aggregate a multiregional time dependent Leslie model showing that the aggregated model has demographic rates depending on the equilibrium proportions of individuals in the different patches.
|Keywords||Philosophy Philosophy of Biology Evolutionary Biology|
|Categories||categorize this paper)|
Setup an account with your affiliations in order to access resources via your University's proxy server
Configure custom proxy (use this if your affiliation does not provide a proxy)
|Through your library|
References found in this work BETA
No references found.
Citations of this work BETA
No citations found.
Similar books and articles
Etienne Kouokam, Pierre Auger, Hassan Hbid & Maurice Tchuente (2008). Effect of the Number of Patches in a Multi-Patch SIRS Model with Fast Migration on the Basic Reproduction Rate. Acta Biotheoretica 56 (1-2):75-86.
Ángel Blasco, Luis Sanz, Pierre Auger & Rafael Bravo de la Parra (2002). Linear Discrete Population Models with Two Time Scales in Fast Changing Environments II: Non-Autonomous Case. Acta Biotheoretica 50 (1):15-38.
Ángel Blasco, Luis Sanz, Pierre Auger & Rafael Bravo de la Parra (2001). Linear Discrete Population Models with Two Time Scales in Fast Changing Environments I: Autonomous Case. Acta Biotheoretica 49 (4):261-276.
Peter Antonelli & Pierre Auger (1995). Corals and Starfish Devastation of the Great Barrier Reef: Aggregation Methods. Acta Biotheoretica 43 (4):481-493.
Luis Sanz & Rafael Bravo de la Parra (2002). The Reliability of Approximate Reduction Techniques in Population Models with Two Time Scales. Acta Biotheoretica 50 (4):297-322.
Ángeles Rincón, Juan Antonio Alonso & Luis Sanz (2009). Reduction of Supercritical Multiregional Stochastic Models with Fast Migration. Acta Biotheoretica 57 (4):479-500.
Pierre Auger & Jean-Christophe Poggiale (1996). Aggregation and Emergence in Hierarchically Organized Systems: Population Dynamics. Acta Biotheoretica 44 (3-4):301-316.
S. Charles, R. Bravo de la Parra, J. P. Mallet, H. Persat & P. Auger (1998). Population Dynamics Modelling in an Hierarchical Arborescent River Network: An Attempt with Salmo Trutta. Acta Biotheoretica 46 (3):223-234.
M. Marvá, R. de la Parra & P. Auger (2012). Reproductive Numbers for Nonautonomous Spatially Distributed Periodic SIS Models Acting on Two Time Scales. Acta Biotheoretica 60 (1-2):139-154.
Eva Sánchez, Rafael Bravo Parra & Pierre Auger (1995). Linear Discrete Models with Different Time Scales. Acta Biotheoretica 43 (4).
Added to index2009-01-28
Total downloads4 ( #424,619 of 1,726,249 )
Recent downloads (6 months)4 ( #183,615 of 1,726,249 )
How can I increase my downloads?