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Adaptive pinning synchronization in fractional-order complex dynamical networks

Author

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  • Chai, Yi
  • Chen, Liping
  • Wu, Ranchao
  • Sun, Jian

Abstract

Synchronization of general complex dynamical networks with fractional-order dynamical nodes is addressed in this paper. Based on the stability theory of fractional-order differential systems and adaptive pinning control, some sufficient local asymptotical synchronization criteria and global asymptotical ones are derived respectively, which succeed in solving the problem about how many nodes are need to be controlled and how much coupling strength should be applied to ensure the synchronization of the entire fractional-order networks. The obtained results are more general and effective than those reported. Moreover, the coupling-configuration matrices and the inner-coupling matrices are not assumed to be symmetric and irreducible. Finally, a numerical simulation is presented to demonstrate the validity and feasibility of the proposed synchronization criteria.

Suggested Citation

  • Chai, Yi & Chen, Liping & Wu, Ranchao & Sun, Jian, 2012. "Adaptive pinning synchronization in fractional-order complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(22), pages 5746-5758.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:22:p:5746-5758
    DOI: 10.1016/j.physa.2012.06.050
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    Cited by:

    1. Xu, Quan & Xu, Xiaohui & Zhuang, Shengxian & Xiao, Jixue & Song, Chunhua & Che, Chang, 2018. "New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics," Applied Mathematics and Computation, Elsevier, vol. 338(C), pages 552-566.
    2. Wang, Yu & Li, Tianzeng, 2015. "Synchronization of fractional order complex dynamical networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 1-12.
    3. Xudong Hai & Guojian Ren & Yongguang Yu & Conghui Xu, 2019. "Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms," Mathematics, MDPI, vol. 7(5), pages 1-17, May.
    4. Cai, Shuiming & Hou, Meiyuan, 2021. "Quasi-synchronization of fractional-order heterogeneous dynamical networks via aperiodic intermittent pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 146(C).
    5. Ma, Jun & Xu, Wenkang & Zhou, Ping & Zhang, Ge, 2019. "Synchronization between memristive and initial-dependent oscillators driven by noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 536(C).
    6. Liang, Song & Wu, Ranchao & Chen, Liping, 2016. "Adaptive pinning synchronization in fractional-order uncertain complex dynamical networks with delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 49-62.
    7. Fang, Mei, 2015. "Synchronization for complex dynamical networks with time delay and discrete-time information," Applied Mathematics and Computation, Elsevier, vol. 258(C), pages 1-11.
    8. Weiyuan Ma & Changpin Li & Jingwei Deng, 2019. "Synchronization in Tempered Fractional Complex Networks via Auxiliary System Approach," Complexity, Hindawi, vol. 2019, pages 1-12, November.
    9. Li, Hong-Li & Hu, Cheng & Jiang, Yao-Lin & Wang, Zuolei & Teng, Zhidong, 2016. "Pinning adaptive and impulsive synchronization of fractional-order complex dynamical networks," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 142-149.
    10. Huang, Conggui & Wang, Fei & Zheng, Zhaowen, 2021. "Exponential stability for nonlinear fractional order sampled-data control systems with its applications," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).

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