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Delay induced Hopf bifurcation in a simplified network congestion control model

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  • Wang, Zhanfeng
  • Chu, Tianguang

Abstract

This paper studies delay induced Hopf bifurcation in a simplified network congestion control model. It is shown that there exists a critical value of delay for the stability of the network. When the value of feedback delay passes through the critical value, the system will lose its stability and Hopf bifurcation will occur. The stability and direction of the bifurcating periodic solutions are determined by perturbation procedure. A numerical example is also worked out to verify the theoretical analysis.

Suggested Citation

  • Wang, Zhanfeng & Chu, Tianguang, 2006. "Delay induced Hopf bifurcation in a simplified network congestion control model," Chaos, Solitons & Fractals, Elsevier, vol. 28(1), pages 161-172.
    • Handle: RePEc:eee:chsofr:v:28:y:2006:i:1:p:161-172
    DOI: 10.1016/j.chaos.2005.05.047
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    Cited by:

    1. 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.
    2. Bigdeli, Nooshin & Haeri, Mohammad, 2009. "Time-series analysis of TCP/RED computer networks, an empirical study," Chaos, Solitons & Fractals, Elsevier, vol. 39(2), pages 784-800.
    3. Huang, Chuangxia & Huang, Lihong & Feng, Jianfeng & Nai, Mingyong & He, Yigang, 2007. "Hopf bifurcation analysis for a two-neuron network with four delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(3), pages 795-812.
    4. Hu, H.Y. & Wang, Z.H., 2009. "Singular perturbation methods for nonlinear dynamic systems with time delays," Chaos, Solitons & Fractals, Elsevier, vol. 40(1), pages 13-27.
    5. Zhu, Wenli & Yi, Zhang, 2007. "Integral input-to-state stability of nonlinear control systems with delays," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 420-427.
    6. Nga, J.H.C. & Iu, H.H.C. & Ling, S.H. & Lam, H.K., 2008. "Comparative study of stability in different TCP/RED models," Chaos, Solitons & Fractals, Elsevier, vol. 37(4), pages 977-987.
    7. Niu, Ben & Wei, Junjie, 2008. "Stability and bifurcation analysis in an amplitude equation with delayed feedback," Chaos, Solitons & Fractals, Elsevier, vol. 37(5), pages 1362-1371.
    8. 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.

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