A novel synchronization scheme called special hybrid projective synchronization (SHPS), in which different state variables can synchronize up to same positive or negative scaling factors, is proposed in this paper. For all the symmetric chaotic systems, research results demonstrate that the SHPS can be realized with a single-term linear controller. Taking unified chaotic system with unknown parameter as an example, based on Lyapunov stability theory, some sufficient conditions and a parameter update law are derived for the implementation of SPHS, which are verified by some corresponding numerical simulations.
Issue Section:
Research Papers
Keywords:
Control
References
1.
Chen
, G. R.
, and Yu
, X. H.
, 2003
, Chaos Control
, Springer
, Berlin
.2.
Pecora
, L. M.
, and Carroll
, T. L.
, 1990
, “Synchronization in Chaotic Systems
,” Phys. Rev. Lett.
, 64
(8
), pp. 821
–824
.3.
Sun
, H. J.
, and Cao
, H. J.
, 2016
, “Synchronization of Two Identical and Non-Identical Rulkov Models
,” Commun. Nonlinear Sci. Numer. Simul.
, 40
, pp. 15
–27
.4.
Rangaprakash
, D.
, and Pradhan
, N.
, 2014
, “Study of Phase Synchronization in Multichannel Seizure EEG Using Nonlinear Recurrence Measure
,” Biomed. Signal Process. Control
, 11
, pp. 114
–122
.5.
Lü
, L.
, Li
, C. R.
, Chen
, L. S.
, and Wei
, L. L.
, 2014
, “Lag Projective Synchronization of a Class of Complex Network Constituted Nodes With Chaotic Behavior
,” Commun. Nonlinear Sci. Numer. Simul.
, 19
(8
), pp. 2843
–2849
.6.
Banerjee
, S.
, Theesar
, S. J.
, and Kurths
, J.
, 2013
, “Generalized Variable Projective Synchronization of Time Delayed Systems
,” Chaos
, 23
(1
), p. 013118
.7.
Ghosh
, D.
, and Banerjee
, S.
, 2013
, “Projective Synchronization of Time-Varying Delayed Neural Network With Adaptive Scaling Factors
,” Chaos, Solitons Fractals
, 53
(53
), pp. 1
–9
.8.
Li
, C. L.
, Xiong
, J. B.
, and Li
, W.
, 2014
, “A New Hyperchaotic System and Its Generalized Synchronization
,” Optik
, 125
(1
), pp. 575
–579
.9.
Geng
, L. L.
, Yu
, Y. G.
, and Zhang
, S.
, 2016
, “Function Projective Synchronization Between Integer-Order and Stochastic Fractional-Order Nonlinear Systems
,” ISA Trans.
, 64
, pp. 34
–46
.10.
Behinfaraz
, R.
, Badamchizadeh
, M. A.
, and Ghiasi
, A. R.
, 2015
, “An Approach to Achieve Modified Projective Synchronization Between Different Types of Fractional-Order Chaotic Systems With Time-Varying Delays
,” Chaos, Solitons Fractals
, 78
, pp. 95
–106
.11.
Wang
, X. Y.
, and Song
, J. M.
, 2009
, “Adaptive Full State Hybrid Projective Synchronization in the Unified Chaotic System
,” Mod. Phys. Lett. B
, 23
(15
), pp. 1913
–1921
.12.
Ghosh
, D.
, and Banerjee
, S.
, 2008
, “Adaptive Scheme for Synchronization-Based Multiparameter Estimation From a Single Chaotic Time Series and Its Applications
,” Phys. Rev. E
, 78
(5
), p. 056211
.13.
Wang
, Z. L.
, Wang
, C.
, Shi
, X. R.
, Ma
, J.
, Tang
, K. M.
, and Cheng
, H. S.
, 2014
, “Realizing Hybrid Synchronization of Time-Delay Hyperchaotic 4D Systems Via Partial Variables
,” Appl. Math. Comput.
, 245
, pp. 427
–437
.14.
Chen
, X. Y.
, Qiu
, J. L.
, Cao
, J. D.
, and He
, H. B.
, 2016
, “Hybrid Synchronization Behavior in an Array of Coupled Chaotic Systems With Ring Connection
,” Neurocomputing
, 173
(Pt. 3), pp. 1299
–1309
.15.
Hu
, M. F.
, Xu
, Z. Y.
, Zhang
, R.
, and Hu
, A. H.
, 2007
, “Adaptive Full State Hybrid Projective Synchronization of Chaotic Systems With the Same and Different Order
,” Phys. Lett. A
, 365
(4
), pp. 315
–327
.16.
Wang
, S.
, Yu
, Y. G.
, and Wen
, G. G.
, 2014
, “Hybrid Projective Synchronization of Time-Delayed Fractional Order Chaotic Systems
,” Nonlinear Anal. Hybrid Syst.
, 11
, pp. 129
–138
.17.
Yu
, Y. G.
, and Li
, H. X.
, 2011
, “Adaptive Hybrid Projective Synchronization of Uncertain Chaotic Systems Based on Backstepping Design
,” Nonlinear Anal. Real World Appl.
, 12
(1
), pp. 388
–393
.18.
Lü
, J. H.
, Chen
, G. R.
, Cheng
, D. Z.
, and Celikovsky
, S.
, 2002
, “Bridge the Gap Between the Lorenz System and the Chen System
,” Int. J. Bifurcation Chaos
, 12
(12
), pp. 2917
–2926
.19.
Qi
, G. Y.
, Du
, S. Z.
, Chen
, G. R.
, Chen
, Z. Q.
, and Yuan
, Z. Z.
, 2005
, “On a Four Dimensional Chaotic System
,” Chaos, Solitons Fractals
, 23
(5
), pp. 1671
–1682
.Copyright © 2017 by ASME
You do not currently have access to this content.
