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Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks

Li, Chengqing, Feng, Bingbing, Li, Shujun, Kurths, Jurgen, Chen, Guanrong (2019) Dynamic Analysis of Digital Chaotic Maps via State-Mapping Networks. IEEE Transactions on Circuits and Systems I: Regular Papers, 66 (6). pp. 2322-2335. ISSN 1549-8328. (doi:10.1109/TCSI.2018.2888688) (Access to this publication is currently restricted. You may be able to access a copy if URLs are provided)

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Abstract

Chaotic dynamics is widely used to design pseudorandom number generators and for other applications such as secure communications and encryption. This paper aims to study the dynamics of discrete-time chaotic maps in the digital (i.e., finite-precision) domain. Differing from the traditional approaches treating a digital chaotic map as a black box with different explanations according to the test results of the output, the dynamical properties of such chaotic maps are first explored with a fixed-point arithmetic, using the Logistic map and the Tent map as two representative examples, from a new perspective with the corresponding state-mapping networks (SMNs). In an SMN, every possible value in the digital domain is considered as a node and the mapping relationship between any pair of nodes is a directed edge. The scale-free properties of the Logistic map's SMN are proved. The analytic results are further extended to the scenario of floating-point arithmetic and for other chaotic maps. Understanding the network structure of a chaotic map's SMN in digital computers can facilitate counteracting the undesirable degeneration of chaotic dynamics in finite-precision domains, helping also classify and improve the randomness of pseudorandom number sequences generated by iterating chaotic maps.

Item Type: Article
DOI/Identification number: 10.1109/TCSI.2018.2888688
Uncontrolled keywords: chaos, digital, pseudorandom number generator, dynamics, complex networks, fixed-point, floating-point, arithmetic, state-mapping networks
Subjects: Q Science > QA Mathematics (inc Computing science) > QA101 Arithmetic
Q Science > QA Mathematics (inc Computing science) > QA 75 Electronic computers. Computer science
Q Science > QA Mathematics (inc Computing science) > QA 76 Software, computer programming,
Q Science > QC Physics > QC20 Mathematical Physics
Divisions: Faculties > University wide - Teaching/Research Groups > Centre for Cyber Security Research
Faculties > Sciences > School of Computing > Security Group
Depositing User: Shujun Li
Date Deposited: 21 Dec 2018 09:16 UTC
Last Modified: 23 Jul 2019 07:56 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/71415 (The current URI for this page, for reference purposes)
Li, Shujun: https://orcid.org/0000-0001-5628-7328
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