Stability Analysis of Internet Congestion Control Model with Compound TCP Under RED

Many applications require fast data transfer over high speed and long distance networks. Compound TCP(CTCP) is a novel congestion control algorithm for high-speed and long delay networks. This paper develops a discrete time dynamic feedback model of a congestion control system with CTCP under random early detection (RED). We find that periodic doubling bifurcation occurs when varying the RED control parameters or other system parameters. The fixed point of congestion control system and the critical value of parameters are determined by theoretical analysis. Moreover, the result of theoretical analysis is proved and bifurcation and chaotic phenomena are numerically studied by using bifurcation diagrams and Lyapunov Exponent.