Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances

Weiyuan Ma; Yujiang Wu; Changpin Li

doi:10.1109/JAS.2016.7510202

Volume 4 Issue 2

Apr. 2017

IEEE/CAA Journal of Automatica Sinica

JCR Impact Factor: 15.3, Top 1 (SCI Q1)

CiteScore: 23.5, Top 2% (Q1)
Google Scholar h5-index: 77， TOP 5

Turn off MathJax

Article Contents

Article Navigation > IEEE/CAA Journal of Automatica Sinica > 2017 > 4(2): 332-339

Weiyuan Ma, Yujiang Wu and Changpin Li, "Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances," IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 332-339, Apr. 2017. doi: 10.1109/JAS.2016.7510202

Citation:

Weiyuan Ma, Yujiang Wu and Changpin Li, "Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances," IEEE/CAA J. Autom. Sinica, vol. 4, no. 2, pp. 332-339, Apr. 2017. doi: 10.1109/JAS.2016.7510202

Citation:

PDF( 3625 KB)

Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances

doi: 10.1109/JAS.2016.7510202

Weiyuan Ma^{1, 2
,
,},
Yujiang Wu^1
,,
Changpin Li^3
,

1.
School of Mathematics and Statistics, Lanzhou University, Lanzhou 730000, China
2.
School of Mathematics and Computer Science, Northwest University for Nationalities, Lanzhou 730000, China
3.
Department of Mathematics, Shanghai University, Shanghai 200444, China

Funds:

This work was supported by National Natural Science Foundation of China 11372170

This work was supported by National Natural Science Foundation of China 11471150

This work was supported by National Natural Science Foundation of China 41465002

and Fundamental Research Funds for the Central Universities 31920130003

More Information

Author Bio:
Yujiang Wu received the B. Sc. and M. Sc. degrees in mathematics at Lanzhou University, Lanzhou, China, in 1982 and 1985, respectively, and he received the Ph. D. degree in mathematics at Shanghai University, Shanghai, China, in 1997. He is currently a professor at the School of Mathematics and Statistics, Lanzhou University, China. His main research interest is scientific computing. Corresponding author of this paper.(e-mail: myjaw@lzu.edu.cn)

Changpin Li received his Ph. D. degree in computational mathematics from Shanghai University, China in 1998. After graduation, he worked in the same university and became a full professor in 2007 and director of the Institute of Computational Mathematics in 2012. Dr. Li is in the broad area of applied theory and computation of bifurcation and chaos, dynamics of fractional ordinary differential equations, dynamics of complex networks, numerical methods and computations of fractional partial differential equations, fractional modeling. Dr Li's current work is focused on fractional modeling of anomalous diffusion with mathematical analysis and numerical calculations. Dr Li has published nearly 100 papers in referred journals with more than 2500 citations. He has co-edited one book published by World Scientific, and has published one book by CRC press. He is on the editorial boards of several journals such as Fractional Calculus and Applied Analysis, International Journal of Bifurcation and Chaos, International Journal of Computer Mathematics, etc. He was also the lead guest editor of European Physical Journal-Special Topics (2011), International Journal of Bifurcation and Chaos (2012), and Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences (2013). He was awarded the Shanghai Natural Science Prize in 2010, Bao Steel Prize in 2011, and Riemann-Liouville Award: Best FDA Paper (theory) in FDA'12 in 2012. (e-mail: lcp@shu.edu.cn)
Corresponding author: Weiyuan Ma received the B. Sc. degree in mathematics at Northwest Normal University, Lanzhou, China, in 2004, and received the M. Sc. degree in mathematics at Lanzhou University, Lanzhou, China, in 2007. He is working toward the Ph. D. degree in computational mathematics at Lanzhou University, Lanzhou, China. He is currently an associate professor at the School of Mathematics and Computer Science, Northwest University for Nationalities, China. His research interests include complex networks, nonlinear systems, and chaos control. (e-mail: mwy2004@126.com)
Received Date: 2015-09-11
Accepted Date: 2016-01-13

Abstract

Abstract

In this paper, the pinning synchronization between two fractional complex dynamical networks with nonlinear coupling, time delays and external disturbances is investigated. A Lyapunov-like theorem for the fractional system with time delays is obtained. A class of novel controllers is designed for the pinning synchronization of fractional complex networks with disturbances. By using this technique, fractional calculus theory and linear matrix inequalities, all nodes of the fractional complex networks reach complete synchronization. In the above framework, the coupling-configuration matrix and the innercoupling matrix are not necessarily symmetric. All involved numerical simulations verify the effectiveness of the proposed scheme.
- External disturbance,
- fractional complex network,
- nonlinear coupling,
- pinning control,
- time delay

FullText(HTML)

References(36)

References

[1]	R. C. Koeller, "Polynomial operators, stieltjes convolution, and fractional calculus in hereditary mechanics, " Acta Mech. , vol. 58, no. 3-4, pp. 251-264, Apr. 1986. doi: 10.1007/s40243-015-0052-y
[2]	P. J. Torvik and R. L. Bagley, "On the appearance of the fractional derivative in the behavior of real materials, " J. Appl. Mech. , vol. 51, no. 2, pp. 294-298, Jun. 1984. https://utsa.influuent.utsystem.edu/en/publications/on-the-appearance-of-the-fractional-derivative-in-the-behavior-of
[3]	O. Heaviside, Electromagnetic Theory. New York, USA: Chelsea, 1971, pp. 1-130.
[4]	I. Podlubny, Fractional Differential Equations. New York, USA: Academic Press, 1998, pp. 201-307.
[5]	I. Grigorenko and E. Grigorenko, "Chaotic dynamics of the fractional Lorenz system, " Phys. Rev. Lett. , vol. 91, no. 3, pp. 034101, Jul. 2003. https://www.researchgate.net/publication/10624262_Chaotic_Dynamics_of_the_Fractional_Lorenz_System
[6]	T. T. Hartley, C. F. Lorenzo, and H. K. Qammer, "Chaos in a fractional order Chuaś system, " IEEE Trans. Circ. Syst. I Fund. Theory Appl. , vol. 42, no. 8, pp. 485-490, Aug. 1995. http://ieeexplore.ieee.org/document/404062/
[7]	C. G. Li and G. R. Chen, "Chaos in the fractional order Chen system and its control, " Chaos Solitons Fractals, vol. 22, no. 3, pp. 549-554, Nov. 2004. http://www.sciencedirect.com/science/article/pii/S0960077904001250
[8]	B. N. Lundstrom, M. H. Higgs, W. J. Spain, and A. L. Fairhall, "Fractional differentiation by neocortical pyramidal neurons, " Nat. Neurosci. , vol. 11, no. 11, pp. 1335-1342, Oct. 2008.
[9]	H. Wang, Y. G. Yu, G. G. Wen, S. Zhang, and J. Z. Yu, "Global stability analysis of fractional-order Hopfield neural networks with time delay, " Neurocomputing, vol. 154, pp. 15-23, Apr. 2015.
[10]	W. H. Deng, C. P. Li, and J. H. Lv, "Stability analysis of linear fractional differential system with multiple time delays, " Nonlinear Dyn. , vol. 48, no. 4, pp. 409-416, Jun. 2007. doi: 10.1007%2Fs11071-006-9094-0
[11]	C. P. Li, W. H. Deng, and D. Xu, "Chaos synchronization of the Chua system with a fractional order, " Phys. A: Stat. Mech. Appl. , vol. 360, no. 2, pp. 171-185, Feb. 2006. http://www.sciencedirect.com/science/article/pii/S0378437105007132
[12]	W. Y. Ma, C. P. Li, and Y. J. Wu, "Impulsive synchronization of fractional Takagi-Sugeno fuzzy complex networks, " Chaos: An Interdisciplinary J. of Nonlinear Sci. , vol. 26, no. 8, pp. 084311, 2016. doi: 10.1063/1.4959535
[13]	X. J. Wu and Y. Lu, "Generalized projective synchronization of the fractional-order Chen hyperchaotic system, " Nonlinear Dyn. , vol. 57, no. 1-2, pp. 25-35, Jul. 2009. http://www.wenkuxiazai.com/doc/086e81ef4afe04a1b071de23.html
[14]	L. P. Chen, Y. Chai, and R. C. Wu, "Linear matrix inequality criteria for robust synchronization of uncertain fractional-order chaotic systems, " Chaos Interdiscip. J. Nonlinear Sci. , vol. 21, no. 4, Article ID 043107, Oct. 2011. doi: 10.1063/1.3650237
[15]	Z. Odibat, "A note on phase synchronization in coupled chaotic fractional order systems, " Nonlinear Anal. Real World Appl. , vol. 13, no. 2, pp. 779-789, Apr. 2012. http://www.sciencedirect.com/science/article/pii/S1468121811002434
[16]	Y. C. Wang, H. G. Zhang, X. Y. Wang, and D. S. Yang, "Networked synchronization control of coupled dynamic networks with time-varying delay, " IEEE Trans. Syst. Man Cybern. B Cybern. , vol. 40, no. 6, pp. 1468-1479, Dec. 2010. http://ieeexplore.ieee.org/document/5422661/
[17]	X. F. Wang and G. R. Chen, "Pinning control of scale-free dynamical networks, " Phys. A: Stat. Mech. Appl. , vol. 310, no. 3-4, pp. 521-531, Jul. 2002. http://www.sciencedirect.com/science/article/pii/S0378437102007720
[18]	F. Sorrentino, M. di Bernardo, F. Garofalo, and G. R. Chen, "Controllability of complex networks via pinning, " Phys. Rev. E, vol. 75, no. 4, pp. 046103, Apr. 2007. http://www.nature.com/nature/journal/v473/n7346/full/nature10011.html
[19]	Y. Liang and X. Y. Wang, "Synchronizability on complex networks via pinning control, " Pramana, vol. 80, no. 4, pp. 593-606, Apr. 2013. http://cat.inist.fr/?aModele=afficheN&cpsidt=27102692
[20]	W. W. Yu, G. R. Chen, J. H. Lv, and J. Kurths, "Synchronization via pinning control on general complex networks, " SIAM J. Control Optim. , vol. 51, no. 2, pp. 1395-1416, Apr. 2013. doi: 10.1137/100781699
[21]	F. Z. Nian and X. Y. Wang, "Optimal pinning synchronization on directed complex network, " Chaos Interdiscip. J. Nonlinear Sci. , vol. 21, no. 4, pp. 043131, Dec. 2011. doi: 10.1063/1.3665699
[22]	Y. Liang and X. Y. Wang, "A method of quickly calculating the number of pinning nodes on pinning synchronization in complex networks, " Appl. Math. Comput. , vol. 246, pp. 743-751, Nov. 2014. https://www.deepdyve.com/lp/elsevier/a-method-of-quickly-calculating-the-number-of-pinning-nodes-on-pinning-UgjoEWItiW
[23]	Y. Liang, X. Y. Wang, and J. Eustace, "Adaptive synchronization in complex networks with non-delay and variable delay couplings via pinning control, " Neurocomputing, vol. 123, pp. 292-298, Jan. 2014. http://www.sciencedirect.com/science/article/pii/S0925231213007625
[24]	Y. H. Xu, C. R. Xie, and D. B. Tong, "Adaptive synchronization for dynamical networks of neutral type with time-delay, " Optik Int. J. Light Electr. Opt. , vol. 125, no. 1, pp. 380-385, Jan. 2014. http://www.sciencedirect.com/science/article/pii/S1468121806000861
[25]	R. R. Cheng, M. S. Peng, and W. B. Yu, "Pinning synchronization of delayed complex dynamical networks with nonlinear coupling, " Phys. A: Stat. Mech. Appl. , vol. 413, pp. 426-431, Nov. 2014. doi: 10.1063/1.2995852
[26]	Y. Tang, Z. D. Wang, and J. A. Fang, "Pinning control of fractional-order weighted complex networks, " Chaos Interdiscip. J. Nonlinear Sci. , vol. 19, no. 1, pp. 013112, Feb. 2009. doi: 10.1063/1.3068350
[27]	L. Pan, W. N. Zhou, J. A. Fang, and D. Q. Li, "Synchronization and anti-synchronization of new uncertain fractional-order modified unified chaotic systems via novel active pinning control, " Commun. Nonlinear Sci. Numer. Simul. , vol. 15, no. 12, pp. 3754-3762, Dec. 2010. http://www.sciencedirect.com/science/article/pii/S0960077907004316
[28]	Y. Chai, L. P. Chen, R. C. Wu, and J. Sun, "Adaptive pinning synchronization in fractional-order complex dynamical networks, " Phys. A: Stat. Mech. Appl. , vol. 391, no. 22, pp. 5746-5758, Nov. 2012. http://www.wenkuxiazai.com/doc/f62ead0bbed5b9f3f90f1c3a.html
[29]	W. Xiang and F. Q. Chen, "Robust synchronization of a class of chaotic systems with disturbance estimation, " Commun. Nonlinear Sci. Numer. Simul. , vol. 16, no. 8, pp. 2970-2977, Aug. 2011. doi: 10.1007%2F978-3-540-69307-9_3
[30]	D. F. Wang, J. Y. Zhang, and X. Y. Wang, "Robust modified projective synchronization of fractional-order chaotic systems with parameters perturbation and external disturbance, " Chin. Phys. B, vol. 22, no. 10, pp. 100504, Apr. 2013. http://cpb.iphy.ac.cn/EN/abstract/abstract55832.shtml
[31]	T. D. Ma and J. Zhang, "Hybrid synchronization of coupled fractional-order complex networks, " Neurocomputing, vol. 157, pp. 166-172, Jun. 2015. https://www.researchgate.net/publication/272375024_Hybrid_synchronization_of_coupled_fractional-order_complex_networks
[32]	L. X. Yang and J. Jiang, "Adaptive synchronization of drive-response fractional-order complex dynamical networks with uncertain parameters, " Commun. Nonlinear Sci. Numer. Simul. , vol. 19, no. 5, pp. 1496-1506, May2014. http://ieeexplore.ieee.org/document/7553164/
[33]	Y. Li, Y. Q. Chen, and I. Podlubny, "Mittag-Leffler stability of fractional order nonlinear dynamic systems, " Automatica, vol. 45, no. 8, pp. 1965-1969, Aug. 2009. http://dl.acm.org/citation.cfm?id=1746943
[34]	M. A. Duarte-Mermoud, N. Aguila-Camacho, J. A. Gallegos, and R. Castro-Linares, "Using general quadratic Lyapunov functions to prove Lyapunov uniform stability for fractional order systems, " Commun. Nonlinear Sci. Numer. Simul. , vol. 22, no. 1-3, pp. 650-659, May2015. http://www.sciencedirect.com/science/article/pii/S100757041400481X
[35]	J. S. Wu and L. C. Jiao, "Synchronization in complex delayed dynamical networks with nonsymmetric coupling, " Phys. A: Stat. Mech. Appl. , vol. 386, no. 1, pp. 513-530, Dec. 2007. http://www.sciencedirect.com/science/article/pii/S0378437107006024
[36]	Q. Song and J. D. Cao, "On pinning synchronization of directed and undirected complex dynamical networks, " IEEE Trans. Circ. Syst. I Regul. Pap. , vol. 57, no. 3, pp. 672-680, Mar. 2010. doi: 10.1007/s11071-010-9865-5

Supplements(0)

Cited By

Proportional views

Proportional views

通讯作者: 陈斌, bchen63@163.com

1.
沈阳化工大学材料科学与工程学院沈阳 110142

Figures(3)

Get Citation

PDF

XML

Article Metrics

Article views (1258) PDF downloads(209)

Pinning Synchronization Between Two General Fractional Complex Dynamical Networks With External Disturbances

doi: 10.1109/JAS.2016.7510202

Abstract

References

Proportional views

Catalog

通讯作者: 陈斌, bchen63@163.com

Article Metrics

Export File

Citation

Format

Content