Didactic application of numerical analysis in nonlinear dynamics: Lorenz model study

Abstract

We describe a practice designed for the numerical study of the Lorenz model that is a central model in the physics of lasers. The didactical objectives pursued in this practice have a dual nature, considering both the introduction to the knowledge of a physical paradigm of deterministic chaos as the training for the use of certain computational tools for its characterization. The method used to achieve programming is finding solutions of the Lorenz model and systematically studying of their temporal evolution using a Mathematica program. In the academic context, the practice is designed to be included in the curriculum of the degree in physics and to facilitate adaptation to other matters in this area, such as quantum optics, fluids, mechanical vibrations, etc. We first study the steady states, and their linear stability, of the Lorenz model equations and then numerically study the different types of dynamic behavior. We pay special attention to the deterministic chaotic behavior and to the sequence of bifurcations leading from periodic to chaotic behavior (routes to chaos).