Matlab Toolbox and GUI for Analyzing One-Dimensional Chaotic Maps

Although the notion of chaos is usually associated with continuous systems, discrete systems can also exhibit chaotic behavior. In fact, discrete systems have less requirements than their continuous counterparts to show chaotic regime, as chaos can be found in simple one-dimensional non-invertible maps. This paper deals specifically with this last kind of systems. To this aim, the author introduces a new Matlab toolbox and GUI (graphical user interface) providing the user with a suitable toolkit for a complete analysis of those systems by computer. The paper describes the software developed to reach these goals, its main features and components and illustrates its performance by applying it to the analysis of important issues regarding one-dimensional maps, such as the calculation of fixed points, the study of their stability and the representation of their bifurcation diagram and Lyapunov exponents, cobweb plots and phase space graphs for various dimensions. In our opinion, the tool described here is very useful in order to carry out such calculations in an efficient and simple way.