Calculating Time Delay and Embedding Dimension Using the C-C Method

File: C-C method for computing time delay and embedding dimension - Implements the C-C correlation integral method to calculate optimal parameters for phase space reconstruction. File: dingyi_lyapunov - Computes Lyapunov exponents through direct definition approach using trajectory divergence rates. File: fencha - Generates Lorenz system bifurcation diagrams by tracking regional maximum values across parameter variations. File: m_test - Determines optimal embedding dimension m using false nearest neighbors algorithm. File: pinghengdian - Calculates equilibrium points of Lorenz systems at specific parameters and computes corresponding eigenvalues. File: poincare - Constructs Poincaré sections for Lorenz systems to analyze system dynamics. File: PSD - Computes power spectral density of Lorenz systems using Fourier transform methods. File: tau_test - Solves for optimal time delay in phase space reconstruction using mutual information or autocorrelation. File: time_test - Performs time-domain analysis of Lorenz systems and generates phase plane plots. File: wolf_lyapunov - Implements Wolf's method for Lyapunov exponent calculation (requires precomputed embedding parameters m and τ). File: xiao_shuju - Applies small data sets method for efficient Lyapunov exponent estimation. File: zheng_jiao - Computes full Lyapunov exponent spectrum using orthogonalization methods. This document contains multiple files and corresponding computational methods for analyzing time delays, embedding dimensions, Lyapunov exponents, and other dynamical properties. These implementations are specifically designed for Lorenz system analysis and eigenvalue computation. The methods enable researchers to determine equilibrium points, generate bifurcation diagrams, compute power spectra, and perform phase space reconstruction under various conditions. Additionally, techniques like time-domain analysis and Poincaré sections facilitate deeper investigation of the Lorenz system's chaotic behavior and dynamical characteristics.