Calculating Time Delay t and Embedding Dimension m

In scientific computing, numerical solution methods are frequently employed for various applications. One common requirement involves calculating time delay t and embedding dimension m parameters. Traditional approaches like autocorrelation function methods and GP (Grassberger-Procaccia) methods can only determine either t or m separately, requiring sequential calculations. This program implements an innovative approach that simultaneously computes both time delay t and embedding dimension m values through coordinated optimization algorithms. The methodology employs mutual information criteria for time delay selection and false nearest neighbor analysis for dimension determination, integrated into a unified computational framework. This integrated approach proves particularly valuable when computing Lyapunov exponents, as accurate Lyapunov calculations fundamentally depend on proper preliminary determination of both t and m parameters. The program's implementation includes phase space reconstruction algorithms with automatic parameter optimization, making it significantly more convenient than traditional segmented approaches. Therefore, this computational tool holds substantial importance in scientific computing applications involving nonlinear dynamics and chaos analysis.