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Design of Digital Chaotic Systems Updated by Random Iterations 2018 ed. [Pehme köide]

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  • Formaat: Paperback / softback, 110 pages, kõrgus x laius: 235x155 mm, kaal: 2226 g, 35 Illustrations, color; 4 Illustrations, black and white; XIII, 110 p. 39 illus., 35 illus. in color., 1 Paperback / softback
  • Sari: SpringerBriefs in Nonlinear Circuits
  • Ilmumisaeg: 08-Mar-2018
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319735489
  • ISBN-13: 9783319735481
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Design of Digital Chaotic Systems Updated by Random Iterations 2018 ed.Suurem pilt
  • Formaat: Paperback / softback, 110 pages, kõrgus x laius: 235x155 mm, kaal: 2226 g, 35 Illustrations, color; 4 Illustrations, black and white; XIII, 110 p. 39 illus., 35 illus. in color., 1 Paperback / softback
  • Sari: SpringerBriefs in Nonlinear Circuits
  • Ilmumisaeg: 08-Mar-2018
  • Kirjastus: Springer International Publishing AG
  • ISBN-10: 3319735489
  • ISBN-13: 9783319735481
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783319735481.html

This brief studies the general problem of constructing digital chaotic systems in devices with finite precision from low-dimensional to high-dimensional settings, and establishes a general framework for composing them. The contributors demonstrate that the associated state networks of digital chaotic systems are strongly connected. They then further prove that digital chaotic systems satisfy Devaney’s definition of chaos on the domain of finite precision. The book presents Lyapunov exponents, as well as implementations to show the potential application of digital chaotic systems in the real world; the authors also discuss the basic advantages and practical benefits of this approach.

The authors explore the solutions to dynamic degradation (including short cycle length, decayed distribution and low linear complexity) by proposing novel modelling methods and hardware designs for two different one-dimensional chaotic systems, which satisfy Devaney’s definition of chaos. They then extend it to a higher-dimensional digital-domain chaotic system, which has been used in image-encryption technology. This ensures readers do not encounter large differences between actual and theoretical chaotic orbits through small errors.

Digital Chaotic Systems serves as an up-to-date reference on an important research topic for researchers and students in control science and engineering, computing, mathematics and other related fields of study.

1 An Introduction to Digital Chaotic Systems Updated by Random Iterations
1(10)
1.1 General Presentation
1(2)
1.2 Mathematical Definitions of Chaos
3(3)
1.2.1 Approaches Similar to Devaney
3(2)
1.2.2 Li-Yorke Approach
5(1)
1.2.3 Topological Entropy Approach
5(1)
1.2.4 Lyapunov Exponent
6(1)
1.3 TestU01
6(1)
1.4 Plan of This Book
7(4)
References
8(3)
2 Integer Domain Chaotic Systems (IDCS)
11(24)
2.1 Description of ROCS
11(5)
2.1.1 Real Domain Chaotic Systems (RDCS)
11(1)
2.1.2 IDCS
12(4)
2.2 Proof of Chaos for IDCS
16(6)
2.2.1 Dense Periodic Points
16(1)
2.2.2 Transitive Property
17(2)
2.2.3 Further Investigations of the Chaotic Behavior of IDCS
19(1)
2.2.4 Relationship Between Iterative Input and Output
20(2)
2.3 Network Analysis of the State Space of ROCS
22(4)
2.3.1 The Corresponding State Transition Diagram and Its Connectivity Analysis for DOCS with N = 3
22(2)
2.3.2 The Corresponding State Transition Diagram and Its Connectivity Analysis for ROCS with N = 4
24(2)
2.4 Circuit Implementation of IDCS
26(9)
References
33(2)
3 Chaotic Bitwise Dynamical Systems (CBDS)
35(12)
3.1 Improvements of Chaotic Bitwise Dynamical Systems (CBDS)
35(3)
3.2 Proof of Chaos for CBDS
38(2)
3.2.1 Dense Periodic Points
38(1)
3.2.2 Transitive Property
39(1)
3.3 Uniformity
40(2)
3.4 TestU01 Statistical Test Results
42(1)
3.5 FPGA-Based Realization of CBDS
43(4)
References
45(2)
4 One-Dimensional Digital Chaotic Systems (ODDCS)
47(12)
4.1 The Structure of One-Dimensional Digital Chaotic Systems
47(3)
4.1.1 The Conventional Iterative Update Mechanism
47(1)
4.1.2 The Iterative Update Mechanism Controlled by Random Sequences
48(2)
4.2 The Connection Between a Chaotic System and Its Strongly Connected Network
50(3)
4.2.1 Transitive Property of ODDCS
51(1)
4.2.2 Dense Periodic Points of ODDCS
52(1)
4.2.3 Chaotic System and Its Strongly Connected Network
53(1)
4.3 Lyapunov Exponents of a Class of ODDCS
53(6)
4.3.1 General Expression of Equivalent Decimal for GF
53(1)
4.3.2 Mathematical Expression for ∂G(y)/∂y
54(1)
4.3.3 Estimating the Lyapunov Exponents
55(2)
Reference
57(2)
5 Higher-Dimensional Digital Chaotic Systems (HDDCS)
59(30)
5.1 Design of HDDCS
59(13)
5.1.1 Higher-Dimensional Integer Domain Chaotic Systems (HDDCS)
59(2)
5.1.2 Description of HDDCS
61(4)
5.1.3 Comparative Study of RDCS, IDCS, CBDS, and HDDCS
65(3)
5.1.4 Network Analysis of the State Space of HDDCS
68(4)
5.2 Chaotic Performance of HDDCS
72(6)
5.2.1 Dense Periodic Points of HDDCS
72(3)
5.2.2 Transitive Property of HDDCS
75(3)
5.3 Lyapunov Exponents of a Class of HDDCS
78(6)
5.3.1 General Expression of Equivalent Decimal for GF
78(2)
5.3.2 Mathematical Expression for ∂gi(y1,y2,...ym)/∂yj
80(1)
5.3.3 Estimating the Lyapunov Exponents
81(3)
5.4 FPGA-Based Real-Time Application of 3D-DCS
84(5)
5.4.1 Design of 3D-DCS in FPGA
84(1)
5.4.2 Design of the FPGA-Based Hardware System for Image Encryption and Decryption
85(3)
5.4.3 FPGA-Based Implementation Result for Image Encryption and Decryption
88(1)
References
88(1)
6 Investigating the Statistical Improvements of Various Chaotic Iterations-Based PRNGs
89(14)
6.1 Various Algorithms for Pseudorandom Number Generation
89(6)
6.1.1 Qualitative Relations Between Topological Properties and Statistical Tests
89(2)
6.1.2 CIPRNGs: Chaotic Iteration-Based PRNG Algorithms
91(4)
6.2 On the Statistical Improvements of CIPRNG Posttreatments
95(5)
6.2.1 First Investigations
95(2)
6.2.2 Variations on the XOR CIPRNG
97(1)
6.2.3 "LETT" CIPRNG (XORshift, XORshift) Version 3
98(1)
6.2.4 The Version 4 Category of CIPRNGs
98(1)
6.2.5 Randomness Quality of CIPRNGs
99(1)
6.3 Practical Security Evaluation
100(3)
7 Conclusions
103(2)
Appendix A Some Weil-Known Generators 105
Dr. Qianxue Wang received her Ph.D. degree (2008-2012) in University of Franche-Comté, Besançon, France. During her thesis, she has written many referenced works on building one-dimensional chaotic system by means of a chaos generation strategy controlled by random sequences. with Prof. Christophe Guyeux. She is then to extend this knowledge to higher-dimensional digital domain chaotic system while conducting post-doctoral research at College of Automation, Guangdong University of Technology, Guangzhou, China, directed by Prof. Simin Yu. She continue this research until now.

Simin Yu received the B.Sc. degree in physics from Yunnan University, Kunming, China in 1983, the M.E. degree in communication and electronic systems, and the Ph.D. degree in nonlinear circuits and systems, both from the South China University of Technology, Guangzhou, China in 1996 and 2001, respectively. Currently, he is a Full Professor in the College of Automation, Guangdong University of Technology, Guangzhou, China. His research interests include nonlinear circuits and systems, chaos theory and its applications, and multimedia chaotic secure communication technology. He has published more than 90 SCI journal papers, receiving more than 1500 SCI citations with H-index 22, 3 academic books, and 20 granted patents in the fields of chaos in electronic circuits and chaotic communications. Christophe Guyeux has a record of about 130 scholarly publications. Since 2010, he published 46 articles in peer-reviewed international journals (as a co-author, including the top-ranked ones in the areas of computer science and interdisciplinary applications, such as IEEE Transactions on Circuits and Systems I, AIP Chaos, or Clinical Infectious Diseases). He is co-author of 1 book chapter and 2 scienti fic monographs. He is also author of 4 software patents, 62 papers that appeared in proceedings of peerreviewed international conferences, and 8 articles in peer-reviewed international and national workshops. The research interests of Pr. Guyeux are in the areas of interdisciplinary sciences and complex systems. He applies techniques from mathematics and/or computer science to solve scienti c questions raised in biology, environment, or computer science elds.