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Volume 4 Issue 2
Apr.  2017

IEEE/CAA Journal of Automatica Sinica

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Article Contents
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

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

doi: 10.1109/JAS.2016.7510202

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
  • 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.


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  • [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
    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
    O. Heaviside, Electromagnetic Theory. New York, USA: Chelsea, 1971, pp. 1-130.
    I. Podlubny, Fractional Differential Equations. New York, USA: Academic Press, 1998, pp. 201-307.
    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
    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/
    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
    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.
    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.
    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
    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
    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
    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
    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
    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
    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/
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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
    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/
    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
    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
    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
    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


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