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Stability analysis for coupled systems with time delay on networks

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  • Chen, Hao
  • Sun, Jitao

Abstract

In this paper, the stability problem for some coupled systems with time delay on networks (CSDNs) is investigated. We provide a systematic method for constructing a global Lyapunov functional for CSDNs by using graph theory. The stability, uniform stability and global uniform stability of the systems are investigated. And by using the Lyapunov functional constructed, some sufficient conditions of stability are obtained.

Suggested Citation

  • Chen, Hao & Sun, Jitao, 2012. "Stability analysis for coupled systems with time delay on networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 528-534.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:3:p:528-534
    DOI: 10.1016/j.physa.2011.08.037
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    References listed on IDEAS

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    1. Song, Qiankun & Wang, Zidong, 2008. "Stability analysis of impulsive stochastic Cohen–Grossberg neural networks with mixed time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(13), pages 3314-3326.
    2. Dai, Yang & Cai, Yunze & Xu, Xiaoming, 2008. "Synchronization criteria for complex dynamical networks with neutral-type coupling delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(18), pages 4673-4682.
    3. Liu, Hui & Chen, Juan & Lu, Jun-an & Cao, Ming, 2010. "Generalized synchronization in complex dynamical networks via adaptive couplings," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(8), pages 1759-1770.
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    Cited by:

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    2. Zhang, Chunmei & Han, Bang-Sheng, 2020. "Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    3. Zhang, Xinhong & Li, Wenxue & Wang, Ke, 2015. "The existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays," Applied Mathematics and Computation, Elsevier, vol. 264(C), pages 208-217.
    4. Hou, Dong & Bai, Xuelin & Zhao, Xin & Li, Wenxue, 2025. "Bipartite synchronization of stochastic complex networks with time-varying delays and multi-links," Chaos, Solitons & Fractals, Elsevier, vol. 198(C).
    5. Bei Zhang & Yonghui Xia & Lijuan Zhu & Haidong Liu & Longfei Gu, 2019. "Global Stability of Fractional Order Coupled Systems with Impulses via a Graphic Approach," Mathematics, MDPI, vol. 7(8), pages 1-10, August.
    6. Zhang, Chunmei & Chen, Tianrui, 2018. "Exponential stability of stochastic complex networks with multi-weights based on graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 602-611.
    7. Yang, Xinrong & Sun, Qilong & Li, Haitao & Kong, Xiangshan, 2023. "Set stabilizability of impulsive probabilistic Boolean networks via impulsive sequence design," Applied Mathematics and Computation, Elsevier, vol. 449(C).
    8. Liu, Yan & Guo, Ying & Li, Wenxue, 2016. "The stability of stochastic coupled systems with time delays and time-varying coupling structure," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 507-520.
    9. 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.

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