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One-Dimensional Nonlinear Model for Producing Chaos
Hua, Zhongyun1; Zhou, Yicong2
Source PublicationIEEE Transactions on Circuits and Systems I: Regular Papers

Motivated by the concept of circuit design in digital circuit, this paper proposes a one-dimensional (1D) nonlinear model (1D-NLM) for producing 1D discrete-time chaotic maps. Our previous works have designed four nonlinear operations of generating new chaotic maps. However, they focus only on discussing individual nonlinear operations and their properties, but fail to consider their relationship among these operations. The proposed 1D-NLM includes these existing nonlinear operations, develops two new nonlinear operations, discusses their relationship among different nonlinear operations, and investigates the properties of different combinations of these operations. To show the effectiveness of 1D-NLM in generating new chaotic maps, as examples, we provide four new chaotic maps and study their dynamics properties from following three aspects: equilibrium point, stability, and bifurcation diagram. Performance evaluations are provided using the Lyapunov exponent, Shannon entropy, correlation dimension, and initial state sensitivity. The evaluation results show that these new chaotic maps have more complex chaotic behaviors than existing ones. To demonstrate the performance of 1D-NLM in practical applications, we use a pseudo-random number generator (PRNG) to compare new and existing chaotic maps. The randomness test results indicate that new chaotic map generated by 1D-NLM shows better performance than existing ones in designing PRNG.

KeywordChaotic Behavior Chaotic Map Chaotification 1d Nonlinear Model
URLView the original
Indexed BySCIE
WOS Research AreaEngineering
WOS SubjectEngineering, Electrical & Electronic
WOS IDWOS:000422660500022
The Source to ArticleWOS
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Cited Times [WOS]:41   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
Faculty of Science and Technology
Corresponding AuthorZhou, Yicong
Affiliation1.School of Computer Science and Technology, Harbin Institute of Technology Shenzhen Graduate School, Shenzhen 518055, China
2.Department of Computer and Information Science, University of Macau, Macau 999078, China
Corresponding Author AffilicationUniversity of Macau
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GB/T 7714
Hua, Zhongyun,Zhou, Yicong. One-Dimensional Nonlinear Model for Producing Chaos[J]. IEEE Transactions on Circuits and Systems I: Regular Papers,2018,65(1):235-246.
APA Hua, Zhongyun,&Zhou, Yicong.(2018).One-Dimensional Nonlinear Model for Producing Chaos.IEEE Transactions on Circuits and Systems I: Regular Papers,65(1),235-246.
MLA Hua, Zhongyun,et al."One-Dimensional Nonlinear Model for Producing Chaos".IEEE Transactions on Circuits and Systems I: Regular Papers 65.1(2018):235-246.
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