Chaos Time Series Toolbox

The Chaos Time Series Toolbox provides multiple approaches for chaos time series prediction and chaos identification. Prediction methods include: Lyapunov exponent calculations (estimating system sensitivity to initial conditions), nonlinear regression techniques (modeling complex nonlinear relationships), support vector machines (SVM-based pattern recognition for chaotic data), and neural network implementations (both feedforward and recurrent architectures for temporal pattern learning). Chaos discrimination methods encompass classical algorithms such as: Hurst exponent analysis (evaluating long-term memory properties), fractal dimension computations (using box-counting or correlation dimension methods), and Lempel-Ziv complexity measurements (quantifying sequence randomness). The selection of appropriate methods depends on the specific characteristics and objectives of the target chaotic time series. When utilizing this toolbox, careful consideration of method applicability and proper implementation techniques is crucial for achieving accurate prediction results. Each method includes optimized parameter settings and validation procedures to ensure reliable analysis outcomes.