Linear discrete population models with two time scales in fast changing environments II: Non-autonomous case
David Bourget (Western Ontario)
David Chalmers (ANU, NYU)
Rafael De Clercq
Jack Alan Reynolds
Learn more about PhilPapers
Acta Biotheoretica 50 (1) (2002)
As the result of the complexity inherent in nature, mathematical models employed in ecology are often governed by a large number of variables. For instance, in the study of population dynamics we often deal with models for structured populations in which individuals are classified regarding their age, size, activity or location, and this structuring of the population leads to high dimensional systems. In many instances, the dynamics of the system is controlled by processes whose time scales are very different from each other. Aggregation techniques take advantage of this situation to build a low dimensional reduced system from which behavior we can approximate the dynamics of the complex original system.In this work we extend aggregation techniques to the case of time dependent discrete population models with two time scales where both the fast and the slow processes are allowed to change at their own characteristic time scale, generalizing the results of previous studies. We propose a non-autonomous model with two time scales, construct an aggregated model and give relationship between the variables governing the original and the reduced systems. We also explore how the properties of strong and weak ergodicity, regarding the capacity of the system to forget initial conditions, of the original system can be studied in terms of the reduced system.
|Keywords||No keywords specified (fix it)|
|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
Eva Sanchez, Pierre Auger & Rafael Bravo de la Parra (1997). Influence of Individual Aggressiveness on the Dynamics of Competitive Populations. Acta Biotheoretica 45 (3-4).
Rachid Mchich, Amal Bergam & Nadia Raïssi (2005). Effects of Density Dependent Migrations on the Dynamics of a Predator Prey Model. Acta Biotheoretica 53 (4).
Peter Antonelli & Pierre Auger (1995). Corals and Starfish Devastation of the Great Barrier Reef: Aggregation Methods. Acta Biotheoretica 43 (4).
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).
Pierre Auger & Jean-Christophe Poggiale (1996). Aggregation and Emergence in Hierarchically Organized Systems: Population Dynamics. Acta Biotheoretica 44 (3-4).
Ángeles Rincón, Juan Antonio Alonso & Luis Sanz (2009). Reduction of Supercritical Multiregional Stochastic Models with Fast Migration. Acta Biotheoretica 57 (4).
Luis Sanz & Rafael Bravo de la Parra (1998). Variables Aggregation in Time Varying Discrete Systems. Acta Biotheoretica 46 (3).
Eva Sánchez, Rafael Bravo Parra & Pierre Auger (1995). Linear Discrete Models with Different Time Scales. Acta Biotheoretica 43 (4).
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).
Added to index2009-01-28
Total downloads2 ( #361,786 of 1,099,957 )
Recent downloads (6 months)1 ( #304,017 of 1,099,957 )
How can I increase my downloads?