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Designing Hyperchaotic Cat Maps with Any Desired Number of Positive Lyapunov Exponents
Hua Z.4; Yi S.3; Zhou Y.3; Li C.2; Wu Y.1
2018-02-01
Source PublicationIEEE Transactions on Cybernetics
ISSN21682267
Volume48Issue:2Pages:463-473
Abstract

Generating chaotic maps with expected dynamics of users is a challenging topic. Utilizing the inherent relation between the Lyapunov exponents (LEs) of the Cat map and its associated Cat matrix, this paper proposes a simple but efficient method to construct an n-dimensional (n-D) hyperchaotic Cat map (HCM) with any desired number of positive LEs. The method first generates two basic n-D Cat matrices iteratively and then constructs the final n-D Cat matrix by performing similarity transformation on one basic n-D Cat matrix by the other. Given any number of positive LEs, it can generate an n-D HCM with desired hyperchaotic complexity. Two illustrative examples of n-D HCMs were constructed to show the effectiveness of the proposed method, and to verify the inherent relation between the LEs and Cat matrix. Theoretical analysis proves that the parameter space of the generated HCM is very large. Performance evaluations show that, compared with existing methods, the proposed method can construct n-D HCMs with lower computation complexity and their outputs demonstrate strong randomness and complex ergodicity.

KeywordCat Map Cat Matrix Chaotification Hyperchaotic Behavior Lyapunov Exponent (Le)
DOI10.1109/TCYB.2016.2642166
URLView the original
Indexed BySCI
Language英语
WOS Research AreaAutomation & Control Systems ; Computer Science
WOS SubjectAutomation & Control Systems ; Computer Science, Artificial Intelligence ; Computer Science, Cybernetics
WOS IDWOS:000422925700002
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Cited Times [WOS]:9   [WOS Record]     [Related Records in WOS]
Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF COMPUTER AND INFORMATION SCIENCE
Affiliation1.University of Southern California, Information Sciences Institute
2.XiangTan University
3.Universidade de Macau
4.Harbin Institute of Technology
Recommended Citation
GB/T 7714
Hua Z.,Yi S.,Zhou Y.,et al. Designing Hyperchaotic Cat Maps with Any Desired Number of Positive Lyapunov Exponents[J]. IEEE Transactions on Cybernetics,2018,48(2):463-473.
APA Hua Z.,Yi S.,Zhou Y.,Li C.,&Wu Y..(2018).Designing Hyperchaotic Cat Maps with Any Desired Number of Positive Lyapunov Exponents.IEEE Transactions on Cybernetics,48(2),463-473.
MLA Hua Z.,et al."Designing Hyperchaotic Cat Maps with Any Desired Number of Positive Lyapunov Exponents".IEEE Transactions on Cybernetics 48.2(2018):463-473.
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