Scaling laws and critical exponents in Smith and Slatkin model

Abstract

In this project we will consider the Smith and Slatkin map that belongs to a set of discrete one-dimensional maps that describe the dynamics of biological populations. What we propose in this project is to construct the bifurcation diagram to analyze the dynamic system. We intend to study the convergence of orbits to the fixed points near the bifurcation of period 1 described by a generalized homogeneous function. We also hope to investigate the convergence of orbits near the period doubling bifurcations. We propose to explore the sensitivity of the system to the initial conditions in the study of the Lyapunov exponents. This work proposal is to continue the project entitled "Dissipation effects, transients and dynamic properties in Discrete mapping", approved by FAPESP in the process 2014/18672-8. (AU)