Mathematica package for analysis and control of chaos in nonlinear systems

Abstract

In this article a symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented. We start by presenting the main properties of chaos and describing some commands with which to obtain qualitative and quantitative measures of chaos, such as the bifurcation diagram and the Lyapunov exponents, respectively. Then we analyze the problem of chaos control and suppression, illustrating the different methodologies proposed in the literature by means of two representative algorithms (linear feedback control and suppression by perturbing the system variables). A novel analytical treatment of these algorithms using the symbolic capabilities of Mathematica is also presented. Well known one- and two-dimensional maps (the logistic and Hénon maps) and flows (the Duffing and Rössler systems) are used throughout the article to illustrate the concepts and algorithms. © 1998 American Institute of Physics.