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Exponential Synchronization of a Class of -Coupled Complex Partial Differential Systems with Time-Varying Delay

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  • Wenhua Xia
  • Yiping Luo
  • Bifeng Zhou
  • Guanghui Liu

Abstract

This paper is concerned with the exponential synchronization for a class of -coupled complex partial differential systems (PDSs) with time-varying delay. The synchronization error dynamic of the PDSs is defined in the -dimensional spatial domain. To achieve synchronization, we added a linear feedback controller. A sufficient condition is derived to ensure the exponential synchronization of the proposed networks using the Lyapunov–Krasovskii stability approach and matrix inequality technology. The proposed system has broad applications. Two example applications are presented in the final section of this paper to verify the proposed theoretical result.

Suggested Citation

  • Wenhua Xia & Yiping Luo & Bifeng Zhou & Guanghui Liu, 2017. "Exponential Synchronization of a Class of -Coupled Complex Partial Differential Systems with Time-Varying Delay," Complexity, Hindawi, vol. 2017, pages 1-9, October.
    • Handle: RePEc:hin:complx:5982365
    DOI: 10.1155/2017/5982365
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    References listed on IDEAS

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    1. Liu, Tao & Dimirovski, Georgi M. & Zhao, Jun, 2008. "Exponential synchronization of complex delayed dynamical networks with general topology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(2), pages 643-652.
    2. Yu, Tianhu & Cao, Dengqing & Yang, Yang & Liu, Shengqiang & Huang, Wenhu, 2016. "Robust synchronization of impulsively coupled complex dynamical network with delayed nonidentical nodes," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 92-101.
    3. Steven H. Strogatz, 2001. "Exploring complex networks," Nature, Nature, vol. 410(6825), pages 268-276, March.
    4. Cheng, Ranran & Peng, Mingshu & Yu, Weibin, 2014. "Pinning synchronization of delayed complex dynamical networks with nonlinear coupling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 426-431.
    5. Zhou, Jin & Xiang, Lan & Liu, Zengrong, 2007. "Synchronization in complex delayed dynamical networks with impulsive effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 684-692.
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