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New complex projective synchronization strategies for drive-response networks with fractional complex-variable dynamics

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  • Xu, Quan
  • Xu, Xiaohui
  • Zhuang, Shengxian
  • Xiao, Jixue
  • Song, Chunhua
  • Che, Chang

Abstract

This paper presents a fully decentralized adaptive scheme to solve the open problem of complex projective synchronization (CPS) in drive-response fractional complex-variable networks (DRFCVNs). Based on local mismatch with the desired state and between coupled nodes, several novel fully decentralized fractional adaptive (FDFA) strategies are proposed to adjust both the feedback control strengths and the coupling weights. By employing Hermitian form Lyapunov functionals and other fractional skills, some sufficient criteria are provided for CPS. Numerical simulation examples are finally employed to illustrate the efficiency of the new synchronization strategies.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:338:y:2018:i:c:p:552-566
    DOI: 10.1016/j.amc.2018.06.055
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    References listed on IDEAS

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    1. Xiaohui Xu & Jiye Zhang & Quan Xu & Zilong Chen & Weifan Zheng, 2017. "Impulsive Disturbances on the Dynamical Behavior of Complex-Valued Cohen-Grossberg Neural Networks with Both Time-Varying Delays and Continuously Distributed Delays," Complexity, Hindawi, vol. 2017, pages 1-12, October.
    2. Huang, Chengdai & Cao, Jinde & Xiao, Min & Alsaedi, Ahmed & Hayat, Tasawar, 2017. "Bifurcations in a delayed fractional complex-valued neural network," Applied Mathematics and Computation, Elsevier, vol. 292(C), pages 210-227.
    3. Li, Hong-Li & Jiang, Yao-Lin & Wang, Zuolei & Zhang, Long & Teng, Zhidong, 2015. "Global Mittag–Leffler stability of coupled system of fractional-order differential equations on network," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 269-277.
    4. Wu, Guo-Cheng & Baleanu, Dumitru & Xie, He-Ping & Chen, Fu-Lai, 2016. "Chaos synchronization of fractional chaotic maps based on the stability condition," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 374-383.
    5. Chao Luo & Xingyuan Wang, 2013. "Chaos Generated From The Fractional-Order Complex Chen System And Its Application To Digital Secure Communication," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 24(04), pages 1-23.
    6. 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.
    7. Zhang, Lei & Song, Qiankun & Zhao, Zhenjiang, 2017. "Stability analysis of fractional-order complex-valued neural networks with both leakage and discrete delays," Applied Mathematics and Computation, Elsevier, vol. 298(C), pages 296-309.
    8. Shi, Yanchao & Cao, Jinde & Chen, Guanrong, 2017. "Exponential stability of complex-valued memristor-based neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 313(C), pages 222-234.
    9. Wu, Guo-Cheng & Baleanu, Dumitru & Luo, Wei-Hua, 2017. "Lyapunov functions for Riemann–Liouville-like fractional difference equations," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 228-236.
    10. Gallegos, Javier A. & Duarte-Mermoud, Manuel A., 2016. "On the Lyapunov theory for fractional order systems," Applied Mathematics and Computation, Elsevier, vol. 287, pages 161-170.
    11. Martínez-Guerra, Rafael & Pérez-Pinacho, Claudia A. & Gómez-Cortés, Gian Carlo & Cruz-Victoria, Juan C., 2015. "Synchronization of incommensurate fractional order system," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 260-266.
    12. Wang, Fei & Yang, Yongqing & Hu, Manfeng & Xu, Xianyun, 2015. "Projective cluster synchronization of fractional-order coupled-delay complex network via adaptive pinning control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 434(C), pages 134-143.
    13. Ding, Dawei & Yan, Jie & Wang, Nian & Liang, Dong, 2017. "Pinning synchronization of fractional order complex-variable dynamical networks with time-varying coupling," Chaos, Solitons & Fractals, Elsevier, vol. 104(C), pages 41-50.
    14. Chen, Xiaofeng & Zhao, Zhenjiang & Song, Qiankun & Hu, Jin, 2017. "Multistability of complex-valued neural networks with time-varying delays," Applied Mathematics and Computation, Elsevier, vol. 294(C), pages 18-35.
    15. Yang, Xujun & Li, Chuandong & Huang, Tingwen & Song, Qiankun, 2017. "Mittag–Leffler stability analysis of nonlinear fractional-order systems with impulses," Applied Mathematics and Computation, Elsevier, vol. 293(C), pages 416-422.
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    Cited by:

    1. Xiaohui Xu & Huanbin Xue & Yiqiang Peng & Quan Xu & Jibin Yang, 2018. "Robust Exponential Stability of Switched Complex-Valued Neural Networks with Interval Parameter Uncertainties and Impulses," Complexity, Hindawi, vol. 2018, pages 1-12, December.
    2. Xiaohui Xu & Jibin Yang & Yanhai Xu, 2019. "Mean Square Exponential Stability of Stochastic Complex-Valued Neural Networks with Mixed Delays," Complexity, Hindawi, vol. 2019, pages 1-20, June.
    3. Xu, Yao & Li, Wenxue, 2020. "Finite-time synchronization of fractional-order complex-valued coupled systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    4. Jinman He & Fangqi Chen & Qinsheng Bi, 2019. "Quasi-Matrix and Quasi-Inverse-Matrix Projective Synchronization for Delayed and Disturbed Fractional Order Neural Network," Complexity, Hindawi, vol. 2019, pages 1-15, April.
    5. Xue, Huanbin & Xu, Xiaohui & Zhang, Jiye & Yang, Xiaopeng, 2019. "Robust stability of impulsive switched neural networks with multiple time delays," Applied Mathematics and Computation, Elsevier, vol. 359(C), pages 456-475.
    6. Wang, Fei & Zheng, Zhaowen, 2019. "Quasi-projective synchronization of fractional order chaotic systems under input saturation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).

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