0
Technical Brief

Dual Combination Synchronization of Six Chaotic Systems

[+] Author and Article Information
Junwei Sun

School of Electric and Information Engineering,
Zhengzhou University of Light Industry,
Zhengzhou 450002, China
e-mails: cgzh@zzuli.edu.cn; junweisun@yeah.net

Suxia Jiang, Guangzhao Cui, Yanfeng Wang

School of Electric and Information Engineering,
Zhengzhou University of Light Industry,
Zhengzhou 450002, China

1Corresponding author.

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received May 23, 2015; final manuscript received September 18, 2015; published online October 23, 2015. Assoc. Editor: Sotirios Natsiavas.

J. Comput. Nonlinear Dynam 11(3), 034501 (Oct 23, 2015) (5 pages) Paper No: CND-15-1137; doi: 10.1115/1.4031676 History: Received May 23, 2015; Revised September 18, 2015

Based on combination synchronization of three chaotic systems and combination–combination synchronization of four chaotic systems, a novel scheme of dual combination synchronization is investigated for six chaotic systems in the paper. Using combined adaptive control and Lyapunov stability theory of chaotic systems, some sufficient conditions are attained to realize dual combination synchronization of six chaotic systems. The corresponding theoretical proofs and numerical simulations are presented to demonstrate the effectiveness and correctness of the dual combination synchronization. Due to the complexity of dual combination synchronization, it will be more secure and interesting to transmit and receive signals in application of communication.

FIGURES IN THIS ARTICLE
<>
Copyright © 2016 by ASME
Topics: Synchronization
Your Session has timed out. Please sign back in to continue.

References

Lorenz, E. N. , 1963, “ Deterministic Nonperiodic Flow,” J. Atmos. Sci., 20(2), pp. 130–141. [CrossRef]
Sun, J. , and Shen, Y. , 2015, “ Quasi-Ideal Memory System,” IEEE Trans. Cybern., 45(7), pp. 1353–1362. [CrossRef] [PubMed]
Pecora, L. M. , and Carroll, T. L. , 1990, “ Complexity and Chaos in Nuclear Dynamics,” Phys. Rev. Lett., 64(8), pp. 821–824. [CrossRef] [PubMed]
Ge, Z. , and Chen, Y. , 2004, “ Synchronization of Unidirectional Coupled Chaotic Systems Via Partial Stability,” Chaos, Solitons Fractals, 21(1), pp. 101–111. [CrossRef]
Chen, D. , Zhao, W. , Liu, X. , and Ma, X. , 2015, “ Synchronization and Antisynchronization of a Class of Chaotic Systems With Nonidentical Orders and Uncertain Parameters,” ASME J. Comput. Nonlinear Dyn., 10(1), p. 011003. [CrossRef]
Koronovskii, A. A. , Moskalenko, O. I. , and Hramov, A. E. , 2010, “ Hidden Data Transmission Using Generalized Synchronization in the Presence of Noise,” Theor. Math. Phys., 55(4), pp. 435–441.
Roy, P. K. , Hens, C. , Grosu, I. , and Dana, S. K. , 2011, “ Engineering Generalized Synchronization in Chaotic Oscillators,” Chaos, 21(1), p. 013106. [CrossRef] [PubMed]
Rosenblum, M. G. , Pikovsky, A. S. , and Kurths, J. , 1996, “ Phase Synchronization of Chaotic Oscillators,” Phys. Rev. Lett., 76(11), pp. 1804–1807. [CrossRef] [PubMed]
Shuai, J. W. , and Durand, D. M. , 1999, “ Phase Synchronization in Two Coupled Chaotic Neurons,” Phys. Lett. A, 264(4), pp. 289–297. [CrossRef]
Ho, M. C. , Hung, Y. C. , and Chou, C. H. , 2002, “ Phase and Anti-Phase Synchronization of Two Chaotic Systems by Using Active Control,” Phys. Lett. A, 296(1), pp. 43–48. [CrossRef]
Zigzag, M. , Butkovski, M. , Englert, A. , Kinzel, W. , and Kanter, I. , 2009, “ Zero-Lag Synchronization of Chaotic Units With Time-Delayed Couplings,” Europhys. Lett., 85(6), p. 60005. [CrossRef]
Liu, P. , 2015, “ Adaptive Hybrid Function Projective Synchronization of General Chaotic Complex Systems With Different Orders,” ASME J. Comput. Nonlinear Dyn., 10(2), p. 021018. [CrossRef]
Zhang, F. , and Liu, S. , 2014, “ Full State Hybrid Projective Synchronization and Parameters Identification for Uncertain Chaotic (Hyperchaotic) Complex Systems,” ASME J. Comput. Nonlinear Dyn., 9(2), p. 021009. [CrossRef]
Sun, J. , Shen, Y. , and Zhang, G. , 2012, “ Transmission Projective Synchronization of Multi-Systems With Non-Delayed and Delayed Coupling Via Impulsive Control,” Chaos, 22(4), p. 043107. [CrossRef] [PubMed]
Hramov, A. E. , and Koronovskii, A. A. , 2005, “ Time Scale Synchronization of Chaotic Oscillators,” Physica D, 206(3), pp. 252–264. [CrossRef]
Luo, R. , Wang, Y. , and Deng, S. , 2011, “ Combination Synchronization of Three Classic Chaotic Systems Using Active Backstepping Design,” Chaos, 21(4), p. 043114. [CrossRef] [PubMed]
Luo, R. , and Wang, Y. , 2012, “ Finite-Time Stochastic Combination Synchronization of Three Different Chaotic Systems and Its Application in Secure Communication,” Chaos, 22(2), p. 023109. [CrossRef] [PubMed]
Sun, J. , Shen, Y. , Zhang, G. , Xu, C. , and Cui, G. , 2012, “ Combination-Combination Synchronization Among Four Identical or Different Chaotic Systems,” Nonlinear Dyn., 73(3), pp. 1211–1222. [CrossRef]
Sun, J. , Shen, Y. , Wang, X. , and Chen, J. , 2014, “ Finite-Time Combination-Combination Synchronization of Four Different Chaotic Systems With Unknown Parameters Via Sliding Mode Control,” Nonlinear Dyn., 76(1), pp. 383–397. [CrossRef]
Sun, J. , Shen, Y. , Yin, Q. , and Xu, C. , 2013, “ Compound Synchronization of Four Memristor Chaotic Oscillator Systems and Secure Communication,” Chaos, 23(1), p. 013140. [CrossRef] [PubMed]
Sun, J. , Yin, Q. , and Shen, Y. , 2014, “ Compound Synchronization for Four Chaotic Systems of Integer Order and Fractional Order,” Europhys. Lett., 106(4), p. 40005. [CrossRef]
Tsimring, L. S. , and Sushchik, M. M. , 1996, “ Multiplexing Chaotic Signals Using Synchronization,” Phys. Lett. A, 213(3), pp. 155–166. [CrossRef]
Liu, Y. , and Davids, P. , 2000, “ Dual Synchronization of Chaos,” Phys. Rev. E, 61(3), pp. 2176–2179. [CrossRef]
Ning, D. , Lu, J. , and Han, X. , 2007, “ Dual Synchronization Based on Two Different Chaotic Systems: Lorenz Systems and Rossler Systems,” J. Comput. Appl. Math., 206(2), pp. 1046–1050. [CrossRef]
Salarieh, H. , and Shahrokhi, M. , 2008, “ Dual Synchronization of Chaotic Systems Via Time-Varying Gain Proportional Feedback,” Chaos, Solitons Fractals, 38(5), pp. 1342–1348. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

Dual combination synchronization of the first variables

Grahic Jump Location
Fig. 2

Dual combination synchronization of the second variables

Grahic Jump Location
Fig. 3

Dual combination synchronization of the third variables

Grahic Jump Location
Fig. 4

Two-dimensional projection of chaotic systems: x11+y11 versus x12+y12

Grahic Jump Location
Fig. 5

Two-dimensional projection of chaotic systems: x11+y11 versus x13+y13

Grahic Jump Location
Fig. 6

Two-dimensional projection of chaotic systems: x22+y22 versus x23+y23

Grahic Jump Location
Fig. 7

Three-dimensional projection of chaotic systems: x21+y21 versus x22+y22 versus x23+y23

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In