模糊熵算法在混沌序列复杂度分析中的应用

为了准确分析混沌序列的复杂性, 采用模糊熵算法(FuzzyEn) 对典型离散混沌系统和连续混沌系统的复杂度进行分析. 与近似熵(ApEn)、 样本熵(SampEn) 和强度统计复杂度算法相比, FuzzyEn算法是一种更有效的混沌复杂度测度算法, 且对相空间维数(m)、 相似容限度(r) 和序列长度(N) 的敏感性、 依赖性更低, 鲁棒性和测度值的连续性更好. 对混沌系统的复杂性分析表明, 连续混沌系统的复杂度远小于离散混沌系统, 但是如果利用高复杂度的离散混沌伪随机序列或经典 m序列对连续混沌系统产生的伪随机序列进行扰动, 则能大大提高混沌序列的复杂性. 为混沌序列在密码学和混沌保密通信中的应用提供了理论依据.

Application of FuzzyEn algorithm to the analysis of complexity of chaotic sequence

To analyze the complexity of chaotic sequence correctly,complexity of systems,including typical discrete chaotic systems and continuous chaotic systems,are investigated based on the FuzzyEn algorithm.Compared with ApEn,SampEn and Intensive statistical complexity algorithm,the FuzzyEn algorithm is an effective measure algorithm for analyzing chaotic sequence complexity,and it has low sensitivity to and slight dependences on phase space dimension(m),similar tolerance(r) and sequence length(N),better robustness and measure value continuities.Results of the complexities of chaotic systems show that the complexity of continuous chaotic systems are much smaller than those of the discrete chaotic systems.However,having been disturbed by high complex discrete chaotic pseudo-random sequences or classical m-series,the pseudo-random sequences of continuous chaotic systems increase their complexities significantly.Our result provides a theoretical basis for the application of chaotic sequences to the field of cryptography and secure communication.