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The Research of Non-cooperative Power Control Method Based on Fairness and User Selection Strategy in Cognitive Radio Networks Read chapter Read first chapter

2019 | OriginalPaper | Chapter

Dynamical Analysis of Nose-Hoover Continuous Chaotic System Based on Gingerbreadman Discrete Chaotic Sequence

Authors : Run Hao, Xuming Ma

Published in: Green Energy and Networking

Publisher: Springer International Publishing

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Abstract

Apply the discrete chaotic sequence of Gingerbreadman System to the only one control parameter of Nose-Hoover continuous chaotic system, can get completely different simulation results. Namely, extracting a part of sequence of Gingerbreadman discrete system randomly, and take this sequence to control Nose-Hoover continuous chaotic system, then make analysis of this new system. Dynamic analysis of the new system, which is based on Nose-Hoover continuous chaotic system under the control of the discrete chaotic sequence of Gingerbreadman system. Compared with the original system carefully, find that phase diagram arising from new system produce obvious changes. We also calculate Lyapunov exponents, compared with the Lyapunov exponents computed from original system, find it also changed. It proved that our new system has chaotic characteristics, provide new method for the chaotic system which are used in the fields of cryptography, secure communication and information security etc.

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previous chapter Dynamics and Synchronization Analysis of Chaotic Characteristic Interconnected Electrical Power System
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Literature
1.
Hall, D., Proudfoot, L.: Memory and identity among irish migrants in nineteenth-century stawell. Comput. Eng. Appl. 44(3), 47–49 (2008)
2.
Masuda, N., Aihara, K.: Cryptosystems with discretized chaotic maps. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 49(1), 28–40 (2002)MathSciNetCrossRef
3.
4.
Bianco M E, Reed D A. Encryption system based on chaos theory: US, US5048086[P] (1991)
5.
Bianco, M.E., Mayhew, G.L.: High speed encryption system and method: US, US 5365588 A[P] (1994)
6.
Deffeyes, K.S.: Encryption system and method. US (1991)
7.
Pecora, L.M., Carroll, T.L.: Paper 9–synchronization in chaotic systems. Phys. Rev. Lett. 64(8), 821–824 (1990)MathSciNetCrossRef
8.
Pecora, L.M., Carroll, T.L.: Driving systems with chaotic signals. Phys. Rev. A 44(4), 2374 (1991)CrossRef
9.
Carroll, T.L., Pecora, L.M.: A circuit for studying the synchronization of chaotic systems. Int. J. Bifurcat. Chaos 2(3), 659–667 (2011)MathSciNetCrossRef
10.
Carroll, T.L., Pecora, L.M.: Cascading synchronized chaotic systems. Phys. D Nonlinear Phenom. 67(1–3), 126–140 (1993)CrossRef
11.
Pecora, L.M., Carroll, T.L.: System for producing synchronized signals, US5245660[P] (1993)
12.
Pecora, L.M., Carroll, T.L.: Cascading synchronized chaotic systems: US, US5379346[P] (1995)
13.
Carroll, T.L., Pecora, L.M., Heagy, J.F.: Synchronization of nonautonomous chaotic systems: Patent Application Department of the Navy, Washington, DC. US5473694[P] (1995)
14.
Cuomo, K.M., Oppenheim, A.V.: Communication using synchronized chaotic systems: US, US5291555[P] (1994)
15.
Cuomo, K.M., Oppenheim, A.V.: Circuit implementation of synchronized chaos with applications to communications. Controlling Chaos 71(1), 153–156 (1996)CrossRef
16.
Murali, K., Lakshmanan, M.: Transmission of signals by synchronization in a chaotic Van der Pol-Duffing oscillator. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdisc. Topics 48(3), R1624–R1626 (1993)
17.
Kocarev, L., Halle, K.S., Eckert, K., et al.: Experimental demonstration of secure communications via chaotic synchronization. Int. J. Bifurcat. Chaos 2(03), 709–713 (1992)CrossRef
18.
Parlitz, U., Chua, L.O., Kocarev, Lj., et al.: Transmission of digital signals by chaotic synchronization. Int. J. Bifurcat. Chaos 2(2), 973–977 (2011)MATH
19.
Papadimitriou, S., Bezerianos, A., Bountis, T.: Secure communication with chaotic systems of difference equations. IEEE Trans. Comput. 46(1), 27–38 (1997)CrossRef
20.
Bernstein, G.M., Lieberman, M.A.: Method and apparatus for generating secure random numbers using chaos: US, US5007087[P] (1991)
21.
22.
Gutowitz, H.A.: Method and apparatus for encryption, decryption and authentication using dynamical systems: US, US5365589[P] (1994)
23.
Pichler, F., Scharinger, J.: Ciphering by Bernoulli-shifts in finite abelian groups
24.
Götz, M., Kelber, K., Schwarz, W.: Discrete-time chaotic encryption systems. I. Statistical design approach. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 44(10), 963–970 (1997)MathSciNetCrossRef
25.
Kotulski, Z., Szczepański, J., et al.: Application of discrete chaotic dynamical systems in cryptography—DCC method. Int. J. Bifurcat. Chaos 9(06), 1121–1135 (2011)MathSciNetCrossRef
26.
27.
Da, L.H., Guo, F.D.: Composite nonlinare descrete chaotic dynamical systems and stream cipher systems. Acta Electronica Sin. 31(8), 1209–1212 (2003)
28.
Fanzhen, W., Guoyuan, Q., Zengqiang, C., et al.: On a four-winged chaotic attractor. Acta Phys. Sin. 56(6), 3137–3144 (2007)MathSciNetMATH
29.
Qi, G., Chen, G., Wyk, M.A.V., et al.: A four-wing chaotic attractor generated from a new 3-D quadratic autonomous system. Chaos, Solitons Fractals 38(3), 705–721 (2008)MathSciNetCrossRef
30.
Chua, L.O., Roska, T.: The CNN paradigm. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 40(3), 147–156 (1993)CrossRef
31.
Suykens, J.A.K., Vandewalle, J.: Generation of n-double scrolls (n = 1, 2, 3, 4…). IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 40(11), 861–867 (1993)CrossRef
32.
Jinhu, H.F., Yu, X., et al.: Generating 3-D multi-scroll chaotic attractors: a hysteresis series switching method. Automatica 40(10), 1677–1687 (2004)MathSciNetCrossRef
33.
Lu, J., Yu, X., Chen, G.: Generating chaotic attractors with multiple merged basins of attraction: a switching piecewise-linear control approach. IEEE Trans. Circ. Syst. I Fundam. Theory Appl. 50(2), 198–207 (2003)MathSciNetCrossRef
34.
Qi, G., Du, S., Chen, G., et al.: On a four-dimensional chaotic system. Chaos, Solitons Fractals 23(5), 1671–1682 (2005)MathSciNetCrossRef
35.
Li, Y.J., Wen, W.Q.: Research of Judging the Chaotic Characteristics with the Lyapunov Exponents. J. Wuhan Univ. Technol. (2004)
36.
May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261(5560), 459 (1976)CrossRef
37.
Huang, Y., Zhang, P., Zhao, W.: Novel grid multiwing butterfly chaotic attractors and their circuit design. IEEE Trans. Circ. Syst. II Express Briefs 62(5), 496–500 (2017)
38.
Ye, X., Mou, J., Luo, C., et al.: Dynamics analysis of Wien-bridge hyperchaotic memristive circuit system. Nonlinear Dyn. 92(3), 923–933 (2018)CrossRef
39.
Holian, B.L., Hoover, W.G.: Numerical test of the Liouville equation. Phys. Rev. 34(5), 4229–4237 (1986)CrossRef
40.
Wolf, A., Swift, J.B., Swinney, H.L., et al.: Determining Lyapounov exponents from a time series. Phys. D Nonlinear Phenom. 16(3), 285–317 (1985)CrossRef
41.
Shui-Sheng, Q.: Study on periodic orbit theory of chaotic attractors (I). J. Circ. Syst. (2003)
42.
Shui-Sheng, Q.: Study on periodic orbit theory of chaotic attractors (II). J. Circ. Syst. (2004)
43.
Qiu, S.S.: A cell model of chaotic attractor. In: IEEE International Symposium on Circuits and Systems. IEEE Xplore, 1997:1033-1036, vol. 2 (2002)
Metadata
Title
Dynamical Analysis of Nose-Hoover Continuous Chaotic System Based on Gingerbreadman Discrete Chaotic Sequence
Authors
Run Hao
Xuming Ma
Copyright Year
2019
Book
Green Energy and Networking

Print ISBN: 978-3-030-21729-7

Electronic ISBN: 978-3-030-21730-3

Copyright Year: 2019

DOI
https://doi.org/10.1007/978-3-030-21730-3_19

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