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Stability and Hopf bifurcation analysis of a TCP/RAQM network with ISMC procedure

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  • Khoshnevisan, Ladan
  • Liu, Xinzhi
  • Salmasi, Farzad R.

Abstract

Transmission control protocol (TCP), which is usually implemented in the transport layer of a communication network, can detect the congestion after its occurrence. But congestion control can be more complicated in networks with wireless access links due to time-varying fading and packet error rate (PER). Thus, it is essential to use robust active queue management (RAQM) to prevent congestion with certain tolerance against serious disturbance of the wireless environment. As the stability of a TCP/RAQM is tremendously related to the transmission delay, this paper focuses on Hopf bifurcation analysis of a network governed by nonlinear delayed differential equations and an integral sliding mode control as a nonlinear RAQM. The transmission delay is assumed as the bifurcation parameter. It is shown that if the delay passes through a critical value, the closed loop system would not remain stable and the Hopf bifurcation occurs. Moreover, based on the normal form theory and the center manifold theorem, the direction and the stability of the bifurcation periodic solutions are determined. Finally, simulation results are given to confirm the analytical achievements and to show the effectiveness of the procedure compared to some recent protocols.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:118:y:2019:i:c:p:255-273
    DOI: 10.1016/j.chaos.2018.11.029
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    References listed on IDEAS

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    1. 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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    3. Xu, Changjin, 2018. "Local and global Hopf bifurcation analysis on simplified bidirectional associative memory neural networks with multiple delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 149(C), pages 69-90.
    4. 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.
    5. Chen, Chang-Kuo & Liao, Teh-Lu & Yan, Jun-Juh, 2009. "Active queue management controller design for TCP communication networks: Variable structure control approach," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 277-285.
    6. Ladan Khoshnevisan & Farzad R. Salmasi, 2016. "A robust and high-performance queue management controller for large round trip time networks," International Journal of Systems Science, Taylor & Francis Journals, vol. 47(7), pages 1586-1597, May.
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