Dynamics of a congestion control model in a wireless access network.pdf

Nonlinear Analysis: Real World Applications 14 (2013) 671–683 Contents lists available at SciVerse ScienceDirect Nonlinear Analysis: Real World Applications journal homepage: /locate/nonrwa Dynamics of a congestion control model in a wireless access network Tao Dong a,b,∗, Xiaofeng Liao a , Tingwen Huang c a State Key Lab. of Power Transmission Equipment and System Security, College of Computer Science, Chongqing University, Chongqing, 400044, China b College of Software and Engineering, Chongqing University of Posts and Telecommunications, Chongqing, 400065, China c Texas AM University at Qatar, Doha, P.O. Box 23874, Qatar a r t i c l e i n f o a b s t r a c t Article history: In this paper, a congestion control algorithm with heterogeneous delays in a wireless access Received 30 November 2011 network is considered. We regard the communication time delay as a bifurcating parameter Accepted 25 July 2012 to study the dynamical behaviors, i.e., local asymptotical stability, Hopf bifurcation and resonant codimension-two bifurcation. By analyzing the associated characteristic equation, Keywords: the Hopf bifurcation occurs when the delay passes through a sequence of critical value. Hopf bifurcation Furthermore, the direction and stability of the bifurcating periodic solutions are derived Congestion control by applying the normal form theory and the center manifold theorem. In the meantime, Stability Wireless access network the resonant codimension-two bifur