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

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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

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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

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References(36)

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

doi: 10.1109/JAS.2016.7510202

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