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Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory

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  • Zhang, Chunmei
  • Han, Bang-Sheng

Abstract

In this paper, a novel kind of stochastic delayed complex networks with multi-weights (SDCNMW) is considered. We first split SDCNMW into multiple stochastic complex networks with single weight. This paper is mainly concerned with the issues of exponential stability for SDCNMW. A global Lyapunov functional is constructed by a graph-theoretical approach based on Kirchhoff’s matrix tree theorem. Razumikhin-type theorem is presented by stochastic stability theory and Razumikhin technique. An easy-verified coefficients-type theorem is also given. Finally, theoretical results are illustrated by stochastic oscillators network successfully.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:538:y:2020:i:c:s0378437119316073
    DOI: 10.1016/j.physa.2019.122827
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    1. Wang, Zengyun & Liu, Xinzhi, 2019. "Exponential stability of impulsive complex-valued neural networks with time delay," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 156(C), pages 143-157.
    2. An, Xin-lei & Zhang, Li & Zhang, Jian-gang, 2015. "Research on urban public traffic network with multi-weights based on single bus transfer junction," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 436(C), pages 748-755.
    3. Shi, Kaibo & Wang, Jun & Zhong, Shouming & Zhang, Xiaojun & Liu, Yajuan & Cheng, Jun, 2019. "New reliable nonuniform sampling control for uncertain chaotic neural networks under Markov switching topologies," Applied Mathematics and Computation, Elsevier, vol. 347(C), pages 169-193.
    4. An, Xin-lei & Zhang, Li & Li, Yin-zhen & Zhang, Jian-gang, 2014. "Synchronization analysis of complex networks with multi-weights and its application in public traffic network," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 412(C), pages 149-156.
    5. Junhao Hu & Xuerong Mao & Chenggui Yuan, 2013. "Razumikhin-Type Theorems on Exponential Stability of SDDEs Containing Singularly Perturbed Random Processes," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, May.
    6. Hongyu Qin & Zhiyong Wang & Fumin Zhu & Jinming Wen, 2018. "Stability Analysis of Additive Runge-Kutta Methods for Delay-Integro-Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-5, June.
    7. 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.
    8. 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.
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    Cited by:

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