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(Electrical Engineering College,Heilongjiang University,Harbin 150080,China)

机构地区：[1]Electrical Engineering College,Heilongjiang University,Harbin 150080,China

出　　处：《Chinese Physics B》2023年第1期207-216,共10页中国物理B（英文版）

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)。

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.

关 键 词：digital chaos dynamic degradation state-mapping graph periodicity analysis 

分 类 号：O415.5[理学—理论物理]