Dynamics of a congestion control model in a wireless access network

In this paper, a congestion control algorithm with heterogeneous delays in a wireless access network is considered. We regard the communication time delay as a bifurcating parameter to study the dynamical behaviors, i.e., local asymptotical stability, Hopf bifurcation and resonant codimension-two bifurcation. By analyzing the associated characteristic equation, the Hopf bifurcation occurs when the delay passes through a sequence of critical value. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. In the meantime, the resonant codimension-two bifurcation is also found in this model. Some numerical examples are finally performed to verify the theoretical results.