Mathematica package for analysis and control of chaos in nonlinear systems

In this article a symbolic Mathematica package for analysis and control of chaos in discrete and continuous nonlinear systems is presented. We start b y presenting the main properties of chaos and describing some commands with which to obtain qualitative and quantitative measures of chaos, such as th e bifurcation diagram and the Lyapunov exponents, respectively. Then we ana lyze the problem of chaos control and suppression, illustrating the differe nt methodologies proposed in the literature by means of two representative algorithms (linear feedback control and suppression by perturbing the syste m variables). A novel analytical treatment of these algorithms using the sy mbolic capabilities of Mathematica is also presented. Well known one- and t wo-dimensional maps (the logistic and Henon maps) and flows (the Duffing an d Rossler systems) are used throughout the article to illustrate the concep ts and algorithms. (C) 1998 American Institute of Physics. [S0894-1866(98)0 1806-9].