Summary: Hopf Bifurcation and Oscillations in Homogeneous
Huibing Yin Paul Wang Tansu Alpcan Prashant G. Mehta
Coordinated Science Laboratory,
Department of Mechanical Science and Engineering,
University of Illinois at Urbana-Champaign,
1206 W. Green Street, Urbana, IL 61801.
Deutsche Telekom Laboratories, Ernst-Reuter-Platz 7, 10587 Germany
Abstract: In this paper, we investigate stability and bifurcation arising in a communication network
model with a large number of homogeneous (symmetric) users and a single bottleneck AQM queue. We
carry out bifurcation analysis to study the effect of user delay and strength of feedback. It is shown that
for any given delay, there exists a critical amount of feedback (due to AQM) at which the equilibrium
loses stability and a limit cycling solution develops via a super-critical Hopf bifurcation. The conclusion
is verified both numerically and analytically.
Communication networks such as the Internet exhibit a wide
variety of complex dynamic behavior. Examples of such com-
plex behavior include dynamic synchronization of the flows