R. Bravo en Parra1⋆, M. Marvá1, E. Sánchez2 and L. Sanz2
1 Departamento de Física y Matemáticas, Universidad de Alcalá 28871 Alcalá de Henares ( Madrid), The country
2 Departamento de Matemática Aplicada, ETSI Industriales Universidad Politécnica de Madrid José Gutiérrez Abascal 2, 28006 Madrid, The country
⋆ Corresponding author. E-mail: firstname.lastname@example.org
Within this work we evaluate the aggregation of variables way of discrete dynamical systems. These techniques contain describing the asymptotic conduct of the complex system involving many coupled variables with the asymptotic conduct of the reduced system formulated when it comes to a couple of global variables. We consider population dynamics models including two processes acting at different time scales. Each process has connected a roadmap describing its effect along its specific time unit. The discrete system encompassing both processes is expressed within the slow time scale creating the map connected towards the slow one and also the k-th iterate from the map connected towards the fast one. Within the straight line situation an effect is mentioned showing the connection between your corresponding asymptotic aspects of both systems, initial and reduced. Within the nonlinear situation, the reduction result establishes the existence, stability and basins of attraction of steady states and periodic solutions of the initial system with the aid of exactly the same aspects of the related reduced system. Several models searching within the primary applying the technique to populations dynamics are collected as one example of the overall results.
Mathematics Subject Classification: 39A11 / 92D25
Key phrases: discrete models / aggregation of variables / time scales / population dynamic.
Resourse:http://www.mmnp-journal.org/articles/mmnp/abs/2013/06/mmnp201386p107/mmnp201386p107.html Key:Decrease in Discrete Dynamical Systems with Applications to Dynamics Population Models