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Chin. Phys. B, 2023, Vol. 32(1): 010501    DOI: 10.1088/1674-1056/ac785c
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A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain

Chunlei Fan(范春雷) and Qun Ding(丁群)
Electrical Engineering College, Heilongjiang University, Harbin 150080, China
Abstract  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.
Keywords:  digital chaos      dynamic degradation      state-mapping graph      periodicity analysis  
Received:  02 January 2022      Revised:  12 June 2022      Accepted manuscript online:  14 June 2022
PACS:  05.45.Ac (Low-dimensional chaos)  
  05.45.Gg (Control of chaos, applications of chaos)  
  05.45.Mt (Quantum chaos; semiclassical methods)  
Fund: Project supported by the National Natural Science Foundation of China (Grant No. 62101178) and the Fundamental Research Funds for the Higher Institutions in Heilongjiang Province, China (Grant No. 2020-KYYWF-1033).
Corresponding Authors:  Chunlei Fan     E-mail:

Cite this article: 

Chunlei Fan(范春雷) and Qun Ding(丁群) A novel algorithm to analyze the dynamics of digital chaotic maps in finite-precision domain 2023 Chin. Phys. B 32 010501

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