Alternative Method for Measure Entropy - Approximate Entropy Approach

This article introduces a straightforward yet effective alternative method for measuring entropy - the approximate entropy approach. We applied this methodology to analyze the complexity of Logistic maps and discovered that Lyapunov exponents and measure entropy values exhibit fundamental linear relationships with complexity. Through computational analysis using sliding window techniques and vector comparison algorithms, we found that the functional relationship between fractal dimension and complexity remains challenging to establish, with unclear connections to both Lyapunov exponents and measure entropy. Nevertheless, this method provides deeper insights into system complexity and offers valuable references for future research. In subsequent studies, we can further investigate these relationships using enhanced pattern recognition algorithms and apply the approximate entropy method to analyze other dynamical systems, potentially incorporating multivariate extensions and different embedding dimension parameters.