Nonautonomous Periodic Difference Equations. With applications in Populations Dynamics and Economics

      Аннотация: Dynamical systems occur in all branches of science. The main goal of the study of a dynamical systems is to understand the long behavior of states in a system for which there is a deterministic rule for how a state evolves. For this reason an understanding of the asymptotic behavior of a dynamical system is probably one of the most relevant problems in sciences based on mathematical modeling. Hence, one of the mathematical concepts of a dynamical system is based on the simple fact that there are certain rules that governs our natural laws. These rules, in general, can be described by discrete mathematical models. This manuscript contains a framework of the theory of nonautonomous (periodic) difference equations. A study of the skew-product dynamical system, periodicity, stability, centre manifold and bifurcation is present. In the second part of the manuscript is present the dynamics of some concrete models that may be used in Ecology, Biology and Economics. The study of these models may be used as a pedagogical examples in a course of discrete dynamical systems.

Ключевые слова: Bifurcation, population dynamics, Stability, Nonautonomous Discrete Dynamical Systems, difference equations