C-C Method and Improved C-C Method for Phase Space Reconstruction

This article presents MATLAB implementations of both the standard C-C method and its improved variant for phase space reconstruction. The program demonstrates high computational efficiency, processing 3000 data points in approximately 3 minutes. Key references include: 1) "Nonlinear dynamics, delay times, and embedding windows.pdf" and 2) "Phase space reconstruction parameter selection based on improved C-C method 4.pdf". The implementation includes the following modular components: 1) C_C_Method_luzhenbo2.m - Main executable file containing the core algorithm implementation 2) LorenzData.dll - Dynamic library for generating discrete Lorenz system data using differential equation solvers 3) DuffingData.dll - Function library for producing Duffing oscillator discrete data through numerical integration 4) RosslerData.dll - Module generating Rossler attractor discrete data with parameterized chaotic dynamics 5) ccFunction.dll - Core computation module calculating S(m,N,r,t) for standard C-C method and S2(m,N,r,t) for improved method using correlation integral algorithms 6) ccFunction_luzhenbo.dll - Enhanced function computing S1(m,N,r,t) specifically for the improved C-C method with optimized statistical calculations The implementation employs time-delay embedding techniques and correlation dimension analysis for optimal phase space reconstruction parameters. Special acknowledgment to Research Forum contributors "Zhang Wenge" and "yangfanboy" for their valuable discussions that inspired improvements in this work.