MATLAB Chaos Toolbox: Complete Free Version with Visible Functions

This article introduces the MATLAB Chaos Toolbox, which implements various methods for chaotic system analysis including the C_C method and Wolf algorithm for calculating largest Lyapunov exponents. Unlike tools provided by Zhenbo Lu, all functions in this toolbox are fully visible with accessible source code, offering a completely free version. The toolbox enables comprehensive chaos analysis for studying diverse phenomena and systems such as weather patterns, stock market behaviors, and complex dynamical systems. These analytical methods provide deeper insights into system dynamics and can assist in forecasting future trends. The toolbox implementation includes key algorithms with MATLAB code structures that allow users to compute chaotic indices efficiently. For instance, the Wolf algorithm implementation uses phase space reconstruction and nearest neighbor tracking to estimate Lyapunov exponents from time series data. The C_C method employs correlation integral calculations to determine optimal embedding parameters. Users can benefit from data visualization tools that plot attractors, bifurcation diagrams, and Lyapunov exponent spectra, facilitating better understanding and analysis of chaotic systems through customizable MATLAB functions and graphical outputs.