A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

作     者：范春雷 丁群 Chunlei Fan;Qun Ding

作者机构：Electrical Engineering CollegeHeilongjiang UniversityHarbin 150080China 

出 版 物：《Chinese Physics B》 (中国物理B（英文版）)

年 卷 期：2023年第32卷第1期

页      面：207-216页

核心收录：

学科分类：0711[理学-系统科学] 07[理学] 0804[工学-仪器科学与技术] 070201[理学-理论物理] 0701[理学-数学] 0702[理学-物理学] 

基　　金：Project supported by the National Natural Science Foundation of China (Grant No.62101178) the Fundamental Research Funds for the Higher Institutions in Heilongjiang Province,China (Grant No.2020-KYYWF-1033) 

主　　题：digital chaos dynamic degradation state-mapping graph periodicity analysis 

摘      要：Chaotic maps are widely used to design pseudo-random sequence generators, chaotic ciphers, and secure communication systems. Nevertheless, the dynamic characteristics of digital chaos in finite-precision domain must be degraded in varying degrees due to the limited calculation accuracy of hardware equipment. To assess the dynamic properties of digital chaos, we design a periodic cycle location algorithm(PCLA) from a new perspective to analyze the dynamic degradation of digital chaos. The PCLA can divide the state-mapping graph of digital chaos into several connected subgraphs for the purpose of locating all fixed points and periodic limit cycles contained in a digital chaotic map. To test the versatility and availability of our proposed algorithm, the periodic distribution and security of 1-D logistic maps and 2-D Baker maps are analyzed in detail. Moreover, this algorithm is helpful to the design of anti-degradation algorithms for digital chaotic dynamics. These related studies can promote the application of chaos in engineering practice.