MATLAB Implementation of False Nearest Neighbors and Cao's Method for Determining Embedding Dimension in Chaotic Systems

This article presents MATLAB source code implementations for determining the optimal embedding dimension of chaotic systems using both the false nearest neighbors method and Cao's method. These techniques are essential for phase space reconstruction in nonlinear time series analysis, helping researchers better understand chaotic system dynamics and improve practical applications. The provided MATLAB code is executable immediately and includes comprehensive implementation details. The false nearest neighbors method identifies genuine neighbors in phase space by checking whether points remain close when increasing the embedding dimension, while Cao's method offers a more robust approach by examining the ratio of distances between neighboring points in consecutive dimensions. Key implementation features include: - Automated parameter selection for different chaotic systems - Distance calculation optimizations using vectorization - Visualization tools for result interpretation - Statistical validation of embedding dimension choices We provide detailed code explanations and practical application examples to help users master these techniques effectively. The code structure includes modular functions for data preprocessing, dimension calculation, and result validation, making it adaptable for various chaotic systems research. This resource aims to support researchers and practitioners working with chaotic systems analysis and nonlinear dynamics.