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Dynamics of the congestion control model in underwater wireless sensor networks with time delay

Author

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  • Dong, Tao
  • Hu, Wenjie
  • Liao, Xiaofeng

Abstract

In this paper, a congestion control model in underwater wireless sensor network with time delay is considered. First, the boundedness of the positive equilibrium, where the samples density is positive for each node and the different event flows coexist, is investigated, which implies that the samples density of sensor node cannot exceed the Environmental carrying capacity. Then, by considering the time delay can be regarded as a bifurcating parameter, the dynamical behaviors, which include local stability and Hopf bifurcation, are investigated. It is found that when the communication time delay passes a critical value, the system loses its stability and a Hopf bifurcation occurs, which means the underwater wireless sensor network will be congested, even collapsed. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some numerical examples are finally performed to verify the theoretical results.

Suggested Citation

  • Dong, Tao & Hu, Wenjie & Liao, Xiaofeng, 2016. "Dynamics of the congestion control model in underwater wireless sensor networks with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 92(C), pages 130-136.
    • Handle: RePEc:eee:chsofr:v:92:y:2016:i:c:p:130-136
    DOI: 10.1016/j.chaos.2016.09.019
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    References listed on IDEAS

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    1. Du, Siyuan & Guo, Chunxiang & Jin, Maozhu, 2016. "Agent-based simulation on tourists’ congestion control during peak travel period using Logit model," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 187-194.
    2. Wen-bo Zhao & Xiao-ke Sun & Huicheng Wang, 2014. "Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-12, April.
    3. Qiu, Bo & Chen, XiQiu & Wu, Qi, 2016. "A key design to prolong lifetime of wireless sensor network," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 491-496.
    4. Liu, Yuan & Wang, RuiXue, 2016. "Study on network traffic forecast model of SVR optimized by GAFSA," Chaos, Solitons & Fractals, Elsevier, vol. 89(C), pages 153-159.
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    Cited by:

    1. Khoshnevisan, Ladan & Liu, Xinzhi & Salmasi, Farzad R., 2019. "Stability and Hopf bifurcation analysis of a TCP/RAQM network with ISMC procedure," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 255-273.
    2. JI, Conghuan & QIAO, Yuanhua & MIAO, Jun & DUAN, Lijuan, 2018. "Stability and Hopf bifurcation analysis of a complex-valued Wilson–Cowan neural network with time delay," Chaos, Solitons & Fractals, Elsevier, vol. 115(C), pages 45-61.

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