Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control
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Authors
Xiaojun Zhang
- School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, P. R. China.
Huilan Yang
- School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, P. R. China.
Shouming Zhong
- School of Mathematics Sciences, University of Electronic Science and Technology of China, Chengdu Sichuan 611731, P. R. China.
Abstract
In this paper, the problem of the lag synchronization between two general complex dynamical networks
with mixed coupling by pinning control is studied. Based on the Lyaponov functional theory and mathematical
analysis method, less conservative conditions of lag synchronization are obtained by adding the
controllers to part of nodes. Moreover, the coupling configuration matrices are not required to be symmetric
or irreducible. It is shown that the lag synchronization of the drive and response systems can be realized
via the linear feedback pinning control and adaptive feedback pinning control. These results remove some
restrictions on the node dynamics and the number of the pinned nodes. Numerical examples are presented
to illustrate the effectiveness of the theoretical results.
Share and Cite
ISRP Style
Xiaojun Zhang, Huilan Yang, Shouming Zhong, Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 6, 4678--4694
AMA Style
Zhang Xiaojun, Yang Huilan, Zhong Shouming, Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control. J. Nonlinear Sci. Appl. (2016); 9(6):4678--4694
Chicago/Turabian Style
Zhang, Xiaojun, Yang, Huilan, Zhong, Shouming. "Lag synchronization of complex dynamical networks with hybrid coupling via adaptive pinning control." Journal of Nonlinear Sciences and Applications, 9, no. 6 (2016): 4678--4694
Keywords
- Lag synchronization
- complex dynamical systems
- pinning control
- hybrid time-varying
MSC
References
-
[1]
R. Albert, H. Jeong, A. L. Barabási, Diameter of the world wide web, Nature, 401 (1999), 130--131
-
[2]
C. A. S. Batista, A. M. Batista, J. A. C. De Pontes, R. L. Viana, S. R. Lopes, Chaotic phase synchronization on scale-free networks of bursting neurons,, Phys. Rev. E, 76 (2007), 016218
-
[3]
A. G. de Oliveira, A. J. Jones, Synchronization of chaotic maps by feedback control and application to secure communications using chaotic neural networks, Int. J. Bifur. Chaos, 8 (1998), 2225--2237
-
[4]
K. Gopalsamy, Stability and oscillations in delay differential equations of population dynamics, Kluwer Academic Publishers, Dordrecht (1992)
-
[5]
K. Gu, V. L. Kharitonov, J. Chen, Stability of time-delay systems, Birkhäuser Boston, Inc., Boston (2003)
-
[6]
W. Guo, Lag synchronization of complex networks via pinning control, Nonlinear Anal. Real World Appl., 12 (2011), 2579--2585
-
[7]
R. A. Horn, C. R. Johnson, Matrix Analysis, Cambridge University Press, Cambridge (1990)
-
[8]
C. Huang, D. W. C. Ho, J. Lu, J. Kurths, Pinning synchronization in T-S fuzzy complex networks with partial and discrete-time couplings, IEEE Trans. Fuzzy Syst., 23 (2015), 1247--1285
-
[9]
S. C. Jeong, D. H. Ji, J. H. Park, S. C. Won, Adaptive synchronization for uncertain chaotic neural networks with mixed time delays using fuzzy disturbance observer, Appl. Math. Comput., 219 (2013), 5984--5995
-
[10]
D. H. Ji, S. C. Jeong, J. H. Park, S. M. Lee, S. C. Won, Adaptive lag synchronization for uncertain complex dynamical network with delayed coupling, Appl. Math. Comput., 218 (2012), 4872-4880
-
[11]
G. P. Jiang, W. K. S. Tang, G. Chen, A state-observer-based approach for synchronization in complex dynamical networks, IEEE Trans. Circuits Syst. I Regul. Pap., 53 (2006), 2739--2745
-
[12]
X. Z. Jin, G. H. Yang, Adaptive pinning synchronization of a class of nonlinearly coupled complex networks, Commun. Nonlinear Sci. Numer. Simul., 18 (2013), 316-326
-
[13]
Y. Jin, S. Zhong, Function projective synchronization in complex networks with switching topology and stochastic effects, Appl. Math. Comput., 259 (2015), 730--740
-
[14]
L. Kuhnert, K. I. Agladze, V. I. Krinsky, Image processing using light-sensitive chemical waves, Nature, 337 (1989), 244--247
-
[15]
H. Li, New criteria for synchronization stability of continuous complex dynamical networks with non-delayed and delayed coupling, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 1027--1043
-
[16]
B. Li, Pinning adaptive hybrid synchronization of two general complex dynamical networks with mixed coupling, Appl. Math. Model., 40 (2016), 2983--2998
-
[17]
C. Li, X. Liao, K. Wong, Chaotic lag synchronization of coupled time-delayed systems and its applications in secure communication, Phys. D, 194 (2004), 187--202
-
[18]
C. Li, W. Sun, J. Kurths, Synchronization between two coupled complex networks, Phys. Rev. E, 76 (2007), 046204
-
[19]
T. L. Liao, N. S. Huang, An observed-based approach for chaotic synchronization with applications to secure communications, IEEE Trans. Circuits Syst. I, 46 (1999), 1144--1150
-
[20]
J. Lu, D. W. C. Ho, J. Cao, J. Kurths, Single impulsive controller for globally exponential synchronization of dynamical networks, Nonlinear Anal. Real World Appl., 14 (2013), 581--593
-
[21]
G. M. Mahmoud, E. E. Mahmoud, Lag synchronization of hyperchaotic complex nonlinear systems, Nonlinear Dynam., 67 (2012), 1613--1622
-
[22]
Q. Miao, Y. Tang, S. Lu, J. Fang, Lag synchronization of a class of chaotic systems with unknown parameters, Nonlinear Dynam., 57 (2009), 107--112
-
[23]
R. E. Mirollo, S. H. Strogatz, Synchronization of pulse-coupled biological oscillators, SIAM J. Appl. Math., 50 (1990), 1645--1662
-
[24]
N. F. Rulkov, M. M. Sushchik, L. S. Tsimring, H. D. I. Abarbanel, Generalized synchronization of chaos in directionally coupled chaotic systems, Phys. Rev. E, 51 (1995), 980--994
-
[25]
K. Shi, X. Liu, H. Zhu, S. Zhong, Y. Liu, C. Yin, Novel integral inequality approach on master-slave synchronization of chaotic delayed Lur'e systems with sampled-data feedback control, Nonlinear dynam., 83 (2016), 1259--1274
-
[26]
Q. Song, J. Cao, On pinning synchronization of directed and undirected complex dynamical networks, IEEE Trans. Circuits Syst. I. Regul. Pap., 57 (2010), 672--680
-
[27]
P. N. Steinmetz, A. Roy, P. J. Fitzgerald, S. S. Hsiao, K. O. Johonson, E. Niebur, Attention modulates synchronized neuronal firing in primate somatosensory cortex, Nature, 404 (2000), 187--190
-
[28]
W. Sun, Z. Chen, J. Lu, S. Chen, Outer synchronization of complex networks with delay via impulse, Nonlinear dynam., 69 (2012), 1751--1764
-
[29]
L. Wang, Z. Yuan, X. Chen, Z. Zhou, Lag synchronization of chaotic systems with parameter mismatches, Commun. Nonlinear Sci. Numer. Simul., 16 (2011), 987--992
-
[30]
D. J. Watts, S. H. Strogatz, Collective dynamics of small world networks, Nature, 393 (1998), 440--442
-
[31]
R. J. Williams, N. D. Martinez, Simple rules yield complex food webs, Nature, 404 (2000), 180--183
-
[32]
J. Wu, L. Jiao, Synchronization in complex delayed dynamical networks with nonsymmetric coupling, Phys. A, 386 (2007), 513--530
-
[33]
Z. Wu, D. Liu, Q. Ye, Pinning impulsive synchronization of complex-variable dynamical network, Commun. Nonlinear Sci. Numer. Simul., 20 (2015), 273--280
-
[34]
Y. Xiao, W. Xu, X. Li, Adaptive complete synchronization of chaotic dynamical networks with unknown and mismatched parameters, Chaos, 17 (2007), 8 pages
-
[35]
Y. Yang, J. Cao, Exponential lag synchronization of a class of chaotic delayed neural networks with impulsive effects, Phys. A, 386 (2007), 492--502
-
[36]
H. Yang, L. Shu, S. Zhong, X. Wang, Extended dissipative exponential synchronization of complex dynamical systems with coupling delay and sampled-data control, J. Franklin Inst., 353 (2016), 1829--1847
-
[37]
W. Yu, G. Chen, J. Cao, Adaptive synchronization of uncertain coupled stochastic complex networks, Asian J. Control, 13 (2011), 418--429
-
[38]
W. Yu, G. Chen, J. Lü, On pinning synchronization of complex dynamical networks, Automatica, 45 (2009), 429--435
-
[39]
Q. J. Zhang, J. A. Lu, Impulsively control complex networks with different dynamical nodes to its trivial equilibrium, Comput. Math. Appl., 57 (2009), 1073--1079
-
[40]
M. Zhao, H. G. Zhang, Z. L. Wang, H. J. Liang, Observer-based lag synchronization between two different complex networks, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 2048--2059
-
[41]
J. Zhou, Q. Wu, L. Xiang, S. Cai, Z. Liu, Impulsive synchronization seeking in general complex delayed dynamical networks, Nonlinear Anal. Hybrid Syst., 5 (2011), 513--524