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Adaptive Pinning Synchronization of Fractional Complex Networks with Impulses and Reaction–Diffusion Terms

Author

Listed:
  • Xudong Hai

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Guojian Ren

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Yongguang Yu

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

  • Conghui Xu

    (Department of Mathematics, Beijing Jiaotong University, Beijing 100044, China)

Abstract

In this paper, a class of fractional complex networks with impulses and reaction–diffusion terms is introduced and studied. Meanwhile, a class of more general network structures is considered, which consists of an instant communication topology and a delayed communication topology. Based on the Lyapunov method and linear matrix inequality techniques, some sufficient criteria are obtained, ensuring adaptive pinning synchronization of the network under a designed adaptive control strategy. In addition, a pinning scheme is proposed, which shows that the nodes with delayed communication are good candidates for applying controllers. Finally, a numerical example is given to verify the validity of the main results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:405-:d:228850
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    References listed on IDEAS

    as
    1. Fang Liu & Qiang Song & Jinde Cao & Jianquan Lu, 2014. "Pinning Synchronization of One-Sided Lipschitz Complex Networks," Discrete Dynamics in Nature and Society, Hindawi, vol. 2014, pages 1-8, April.
    2. 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.
    3. Lu, Jun Guo, 2008. "Global exponential stability and periodicity of reaction–diffusion delayed recurrent neural networks with Dirichlet boundary conditions," Chaos, Solitons & Fractals, Elsevier, vol. 35(1), pages 116-125.
    4. Feng, Jianwen & Yang, Pan & Zhao, Yi, 2016. "Cluster synchronization for nonlinearly time-varying delayed coupling complex networks with stochastic perturbation via periodically intermittent pinning control," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 52-68.
    5. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    6. Li, Chunguang & Chen, Guanrong, 2004. "Synchronization in general complex dynamical networks with coupling delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 263-278.
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    Cited by:

    1. Yi Liang & Yunyun Deng & Chuan Zhang, 2023. "Outer Synchronization of Two Muti-Layer Dynamical Complex Networks with Intermittent Pinning Control," Mathematics, MDPI, vol. 11(16), pages 1-15, August.
    2. M. Hymavathi & Tarek F. Ibrahim & M. Syed Ali & Gani Stamov & Ivanka Stamova & B. A. Younis & Khalid I. Osman, 2022. "Synchronization of Fractional-Order Neural Networks with Time Delays and Reaction-Diffusion Terms via Pinning Control," Mathematics, MDPI, vol. 10(20), pages 1-18, October.

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