Liner discrete population models with two time scales in fast changing environments II:non-autonomous case

摘要

As the result of the complexity inherent in nature,mathematical model's empolyed 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 system.In many instances,the dynamics of the system in 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 timw scale,generalizing the results of previous studies.We propose a non-autonomous model with two time scales,construct an aggregated model and give relationships betweem 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 of forget initial conditions,of the original system can be studied in terms of the reduced system.