Hopf bifurcation and oscillations in a communication network with heterogeneous delays

Huibing Yin, Paul Wang, Tansu Alpcan, Prashant G. Mehta

Research output: Contribution to journalArticlepeer-review


In this paper, we investigate stability, bifurcation and oscillations arising in a single-link communication network model with a large number of heterogeneous users adopting a Transmission Control Protocol (TCP)-like rate control scheme with an Active Queue Management (AQM) router. In the system considered, different user delays are known and fixed but taken from a given distribution. It is shown that for any given distribution of delays, there exists a critical amount of feedback (due to AQM) at which the equilibrium loses stability and a limit cycling solution develops via a Hopf bifurcation. The nature (criticality) of the bifurcation is investigated with the aid of Lyapunov-Schmidt perturbation method. The results of the analysis are numerically verified and provide valuable insights into dynamics of the AQM control system.

Original languageEnglish (US)
Pages (from-to)2358-2367
Number of pages10
Issue number10
StatePublished - Oct 2009


  • Communication networks
  • Dynamic stability
  • Nonlinear analysis
  • Perturbation analysis
  • Time delay

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering


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