Research Papers

Compound Synchronization Based on Memristive Cellular Neural Network of Chaos System

[+] Author and Article Information
Xiaohong Zhang

School of Information Engineering,
Jiangxi University of Science and Technology,
Ganzhou 341000, China
e-mail: xiaohongzh@263.net

Linyu Liao

School of Information Engineering,
Jiangxi University of Science and Technology,
Ganzhou 341000, China

Contributed by the Design Engineering Division of ASME for publication in the JOURNAL OF COMPUTATIONAL AND NONLINEAR DYNAMICS. Manuscript received July 15, 2015; final manuscript received August 14, 2016; published online December 5, 2016. Assoc. Editor: Bogdan I. Epureanu.

J. Comput. Nonlinear Dynam 12(3), 031002 (Dec 05, 2016) (9 pages) Paper No: CND-15-1218; doi: 10.1115/1.4034565 History: Received July 15, 2015; Revised August 14, 2016

As a especial type of synchronous method, compound synchronization is designed by multiple drive systems and response systems. In this paper, a new type of compound synchronization of three drive systems and two response systems is investigated. According to synchronous control of five memristive cellular neural networks (CNNs), the theoretical analysis and demonstration are given out by using Lyapunov stability theory. The corresponding numerical simulations and synchronous performance analysis are supplied to verify the feasibility and scalability of compound synchronization design.

Copyright © 2017 by ASME
Your Session has timed out. Please sign back in to continue.


Mahmoud, G. M. , and Mahmoud, E. E. , 2010, “ Complete Synchronization of Chaotic Complex Nonlinear Systems With Uncertain Parameters,” Nonlinear Dyn., 62(4), pp. 875–882. [CrossRef]
Wen, S. , Bao, G. , Zeng, Z. , Chene, Y. , and Huang, T. , 2013, “ Global Exponential Synchronization of Memristor-Based Recurrent Neural Networks With Time-Varying Delays,” Neural Networks, 48, pp. 195–203. [CrossRef] [PubMed]
Koronovskii, A. A. , Moskalenko, O. I. , and Hramov, A. E. , 2010, “ Hidden Data Transmission Using Generalized Synchronization in the Presence of Noise,” Tech. Phys., 55(4), pp. 435–441. [CrossRef]
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]
Li, D. , Li, X. , Cui, D. , and Li, Z. , 2011, “ Phase Synchronization With Harmonic Wavelet Transform With Application to Neuronal Populations,” Neurocomputing, 74(17), pp. 3389–3403. [CrossRef]
Odibat, Z. , 2012, “ A Note on Phase Synchronization in Coupled Chaotic Fractional Order Systems,” Nonlinear Anal.: Real World Appl., 13(2), pp. 779–789. [CrossRef]
Bhowmick, S. K. , Pal, P. , Roy, P. K. , and Dana, S. K. , 2012, “ Lag Synchronization and Scaling of Chaotic Attractor in Coupled System,” Chaos, 22(2), p. 023151. [CrossRef] [PubMed]
Yu, J. , Hu, C. , Jiang, H. , and Teng, Z. , 2012, “ Exponential Lag Synchronization for Delayed Fuzzy Cellular Neural Networks Via Periodically Intermittent Control,” Math. Comput. Simul., 82(5), pp. 895–908. [CrossRef]
Wang, X. Y. , and Wang, M. J. , 2010, “ Projective Synchronization of Nonlinear-Coupled Spatiotemporal Chaotic Systems,” Nonlinear Dyn., 62(3), pp. 567–571. [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]
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]
Wu, A. , 2014, “ Hyperchaos Synchronization of Memristor Oscillator System Via Combination Scheme,” Adv. Differ. Equations, 2014(1), pp. 1–11. [CrossRef]
Sun, J. , Shen, Y. , Zhang, G. , Xu, C. , and Cui, G. , 2013, “ Combination–Combination Synchronization Among Four Identical or Different Chaotic Systems,” Nonlinear Dyn., 73(3), pp. 1211–1222. [CrossRef]
Jin-E, Z. , 2014, “ Combination-Combination Hyperchaos Synchronization of Complex Memristor Oscillator System,” Math. Probl. Eng., 2014, p. 591089. [CrossRef]
Chua, L. O. , 1971, “ Memristor—The Missing Circuit Element,” IEEE Trans. Circuit Theory, 18(5), pp. 507–519. [CrossRef]
Itoh, M. , and Chua, L. O. , 2008, “ Memristor Oscillators,” Int. J. Bifurcation Chaos, 18(11), pp. 3183–3206. [CrossRef]
Bao, B. C. , Liu, Z. , and Xu, J. P. , 2010, “ Steady Periodic Memristor Oscillator With Transient Chaotic Behaviors,” Electron. Lett., 46(3), pp. 228–230. [CrossRef]
Wen, S. , Zeng, Z. , Huang, T. , and Chen, Y. , 2013, “ Fuzzy Modeling and Synchronization of Different Memristor-Based Chaotic Circuits,” Phys. Lett. A, 377(34), pp. 2016–2021. [CrossRef]
Chua, L. O. , and Yang, L. , 1988, “ Cellular Neural Networks: Applications,” IEEE Trans. Circuits Syst., 35(10), pp. 1273–1290. [CrossRef]
Benettin, G. , Galgani, L. , Giorgilli, A. , and Strelcyn, J.-M. , 1980, “ Lyapunov Characteristic Exponents for Smooth Dynamical Systems and for Hamiltonian Systems; A Method for Computing all of Them. Part 1: Theory,” Meccanica, 15(1), pp. 9–20. [CrossRef]


Grahic Jump Location
Fig. 1

Compound synchronization scheme of five systems

Grahic Jump Location
Fig. 2

Compound synchronization summary of Corollaries 1–8

Grahic Jump Location
Fig. 3

The chaotic attractors from system (14)

Grahic Jump Location
Fig. 5

Synchronization error curves with e1,e2,e3

Grahic Jump Location
Fig. 4

Waveforms of combination x(x2i+x3i)1i and y1i+y2i(i=1,2,3) between drive systems (15) and response systems (16): (a) x(x21+x31)11 and y11+y21, (b) x(x22+x32)12 and y12+y22, and (c) x(x23+x33)13 and y13+y23



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