Linear stability and Hopf bifurcation in an exponential RED algorithm model

Abstract

We consider a novel congestion control model, i.e., the exponential RED algorithm with a single link and single source. Using the gain parameter of the system instead of the delay as the bifurcation parameter, the linear stability and Hopf bifurcation are investigated, and the stability and direction of the Hopf bifurcation are determined by employing the normal form method and the center manifold reduction. Numerical simulations are carried out to illustrate our theoretical results.