Complexity Analysis of Three-Dimensional Fractional-Order Chaotic System Based on Entropy Theory

Complexity analysis of fractional-order chaotic system is an interesting topic in recent years. How to measure the complexity of fractional-order chaotic system correctly and effectively is the basis of its theoretical analysis and engineering application. In this paper, complexity analysis of three-dimensional fractional-order chaotic system based on multivariate multiscale fuzzy entropy (mvMFE), multivariate multiscale sample entropy (mvMSE) and multivariate multiscale dispersion entropy (mvMDE) respectively is proposed. In the case of single parameter change, different entropy such as mvMFE, mvMSE and mvMDE are used to analyze how complexity varies with parameter. In the case of two parameters change, the change of complexity is analyzed by the chromatomap which takes two parameters as independent variable, and mvMFE, mvMSE, and mvMDE as the dependent variable when the two parameters change simultaneously. Aiming at the performance problem when the complexity of three-dimensional fractional-order chaotic system is analyzed by mvMFE, mvMSE, and mvMDE, the maximum complexity under single parameter and the detection area under two parameters are used as indicators. The result shows that the performance of mvMDE is the best, and the nonlinear term in the mathematical model of fractional-order chaotic system is positively correlated with the complexity of the system. This will provide a new method for measuring the complexity of fractional-order chaotic system, and lay the basis of theoretical analysis and practical application of fractional chaotic system in the fields of image encryption, sound encryption, image compression-encryption technique, and secure communication.