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

doi:10.1088/1674-1056/ac785c

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: 2020021@hlju.edu.cn

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

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