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Synchronization for a Class of Fractional-order Linear Complex Networks via Impulsive Control

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  • Control Theory and Applications
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Abstract

Up to now, the research topic about fractional-order complex networks is mainly focused on the synchronization. In this paper, synchronization for a class of fractional-order linear complex networks is realized via impulsive control. The general expression of solution for a fractional-order impulsive error system is deduced by utilizing iteration algorithm. Some inequality conditions are established to guarantee that the largest Lyapunov exponents of each node are negative, which means that the corresponding error system is asymptotic stable and synchronization is realized. It is the first time to achieve the synchronization of fractional-order systems based on the largest Lyapunov exponent. Finally, examples are present to illustrate the validity and effectiveness of proposed conclusions. Numerical simulations also indicate that the fractional-order parameter has a great influence on the largest Lyapunov exponent, although it is not reflected in the theoretical analysis.

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References

  1. K. B. Shi, X. Z. Liu, H. Zhu, S. M. Zhong, Y. Zeng, and C. Yin, “Novel delay-dependent master-slave synchronization criteria of chaotic Lur’e systems with time-varying-delay feedback control,” Applied Mathematics and Computation, vol. 282, pp. 137–154, 2016.

    Article  MathSciNet  Google Scholar 

  2. Q. Wang and D.-L. Qi, “Synchronization for fractional order chaotic systems with uncertain parameters,” Control Theory and Applications, vol. 14, no. 1, pp. 211–216, February 2016.

    Google Scholar 

  3. K. B. Shi, Y. Y. Tang, X. Z. Liu, and S. M. Zhong, “Nonfragile sampled-data robust synchronization of uncertain delayed chaotic Lurie systems with randomly occurring controller gain fluctuation,” ISA Transactions, vol. 66, pp. 185–199, January 2017.

    Article  Google Scholar 

  4. S. Song, X.-N. Song, N. Pathak, and I. T. Balsera, “Multiswitching adaptive synchronization of two fractional-order chaotic systems with different structure and different order,” Control Theory and Applications, vol. 15, no. 4, pp. 1524–1535, August 2017.

    Google Scholar 

  5. K. Z. Guan, “Global power-rate synchronization of chaotic neural networks with proportional delay via impulsive control,” Neurocomputing, vol. 283, pp. 256–265, March 2018.

    Google Scholar 

  6. Y. Tang, F. Qian, H. J. Gao, and J. Kurths, “Synchronization in complex networks and its application-A survey of recent advances and challenges,” Annual Reviews in Control, vol. 38, no. 2, pp. 184–198, September 2014.

    Article  Google Scholar 

  7. X.Wu, D. Lai, and H. Lu, “Generalized synchronization of the fractional-order Chaos in weighted complex dynamical networks with nonidentical nodes,” Nonlinear Dynamics, vol. 69, no. 1–2, pp. 667–683, December 2012.

    MathSciNet  MATH  Google Scholar 

  8. J. Yu, C. Hu, H. J. Jiang, and X. L. Fan, “Projective synchronization for fractional neural networks,” Neural Network, vol. 49, pp. 87–95, January 2014.

    Article  MATH  Google Scholar 

  9. J. Wang and C. Zeng, “Synchronization of fractional-order linear complex networks,” ISA Transactions, vol. 55, no. 1, pp. 129–134, March 2015.

    Article  Google Scholar 

  10. S. Liang, R. Wu, and L. Chen, “Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay,” Physica A: Statistical Mechanics and its Applications, vol. 44, pp. 49–62, February 2016.

    MathSciNet  MATH  Google Scholar 

  11. J. W. Wang and Y. B. Zhang, “Network synchronization in a population of star-coupled fractional nonlinear oscillators,” Physics Letters A, vol. 374, no. 13–14, pp. 1464–1468, March 2010.

    Article  MATH  Google Scholar 

  12. Y. Tang and J. A. Fang, “Reply to the comment on “Synchronization of N-coupled fractional-order chaotic systems with ring connection”,” Communications in Nonlinear Science and Numerical Simulation, vol. 15, no. 12, pp. 4244–4245, December 2010.

    Article  MathSciNet  MATH  Google Scholar 

  13. S. S. Delshad, M. M. Asheghan, and M. H. Behesh, “Synchronization of N-coupled incommensurate fractionalorder chaotic systems with ring connection,” Communications in Nonlinear Science and Numerical Simulation, vol. 16, no. 9, pp. 3815–3824, September 2011.

    Article  MathSciNet  MATH  Google Scholar 

  14. T. D. Ma, J. Zhang, Y. C. Zhou, and H. Y. Wang, “Adaptive hybrid projective synchronization of two coupled fractional-order complex networks with different sizes,” Neurocomputing, vol. 164, no. C, pp. 182–189, September 2015.

    Google Scholar 

  15. R. Rakkiyappan, J. G. Cao, and G. Velmurugan, “Existence and uniform stability analysis of fractional-order complexvalued neural networks with time delays,” IEEE Transactions on Neural Networks and Learning Systems, vol. 26, no. 1, pp. 84–97, March 2014.

    Article  Google Scholar 

  16. T. D. Ma and J. Zhang, “Hybrid synchronization of coupled fractional-order complex networks,” Neurocomputing, vol. 157, pp. 166–172, June 2015.

    Article  Google Scholar 

  17. Q. X. Fang and J. G. Peng, “Synchronization of fractionalorder linear complex networks with directed coupling topology,” Physica A: Statistical Mechanics and its Applications, vol. 490, pp. 542–553, September 2018.

    Article  MathSciNet  Google Scholar 

  18. Y. Yang, Y. He, Y. Wang, and M. Wu, “Stability analysis of fractional-order neural networks: An LMI approach,” Neurocomputing, vol. 285, pp. 582–93, April 2018.

    Google Scholar 

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Authors and Affiliations

  1. School of Electric and Information Engineering, Zhengzhou University of Light Industry, No.5 Dongfeng Road, Zhengzhou, Henan Province, China

    Na Liu, Jie Fang, Wei Deng, Zhen-Jun Wu & Guo-Qiang Ding

Authors
  1. Na Liu
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  2. Jie Fang
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  3. Wei Deng
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  4. Zhen-Jun Wu
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  5. Guo-Qiang Ding
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Corresponding author

Correspondence to Na Liu.

Additional information

Recommended by Associate Editor Ho Jae Lee under the direction of Editor PooGyeon Park. This work is supported by National Natural Science Foundation of China under Grant 61775198 and 61603348. The work is also sponsored by Natural Science Foundation of Henan Province under Grant 162300410323, 182102210160 and Doctor Scientific Research Fund of Zhengzhou University of Light Industry under Grant No. 2014BSJJ047.

Na Liu received her Ph.D. degree in Control Theory and Control Engineering from Huazhong University of Science and Technology in 2010. Her research interests include nonlinear control, chaos, and complex networks.

Jie Fang received her Ph.D. degree in Control Theory and Control Engineering from Nanjing University of Aeronautics and Astronautics in 2012. Her research interests include nonlinear control, chaos, and complex networks.

Wei Deng received her M.S. degree in Electrician Theory and New Technology from Zhengzhou University in 2007. Her research interests include nonlinear control, chaotic synchronization and control.

Zhen-Jun Wu received his Ph.D. degree in Power Electronics and Power Transmission from Chinese academy of sciences in 2009. His research interests include nonlinear control, power quality and electromagnetic compatibility.

Guo-Qiang Ding received his Ph.D. degree in Navigation, Guidance and Control, from Harbin Engineering University in 2010. His research interests include navigation automation technology, nonlinear optimal filtering theory and algorithm, computer integrated measurement.

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Liu, N., Fang, J., Deng, W. et al. Synchronization for a Class of Fractional-order Linear Complex Networks via Impulsive Control. Int. J. Control Autom. Syst. 16, 2839–2844 (2018). https://doi.org/10.1007/s12555-017-0403-9

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  • DOI: https://doi.org/10.1007/s12555-017-0403-9

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