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Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network

Author

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  • Wen-bo Zhao
  • Xiao-ke Sun
  • Huicheng Wang

Abstract

We drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. 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 examples and numerical simulations are presented to show the feasibility of the theoretical results.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnlaaa:632564
    DOI: 10.1155/2014/632564
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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. Lu, Qiu & Xiao, Min & Tao, Binbin & Huang, Chengdai & Shi, Shuo & Wang, Zhengxin & Jiang, Guoping, 2019. "Complex dynamic behaviors of a congestion control system under a novel PD1n control law: Stability, bifurcation and periodic oscillations," Chaos, Solitons & Fractals, Elsevier, vol. 126(C), pages 242-252.
    3. Pei, Lijun & Wu, Fanxin, 2021. "Periodic solutions, chaos and bi-stability in the state-dependent delayed homogeneous Additive Increase and Multiplicative Decrease/Random Early Detection congestion control systems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 871-887.
    4. 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.

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