Hopf and resonant double Hopf bifurcation in congestion control algorithm with heterogeneous delays

Abstract

The congestion control algorithm, which has dynamic adaptations at both user ends and link ends, with heterogeneous delays is considered and analyzed. Some general stability criteria involving the delays and the system parameters are derived by generalized Nyquist criteria. Furthermore, by choosing one of the delays as the bifurcation parameter, and when the delay exceeds a critical value, a limit cycle emerges via a Hopf bifurcation. Resonant double Hopf bifurcation is also found to occur in this model. An efficient perturbation-incremental method is presented to study the delay-induced resonant double Hopf bifurcation. For the bifurcation parameter close to a double Hopf point, the approximate expressions of the periodic solutions are updated iteratively by use of the perturbation-incremental method. Simulation results have verified and demonstrated the correctness of the theoretical results.

Local stability and Hopf bifurcation of two-dimensional nonlinear descriptor system

“…8. If τ = 0.8696 > τ 0 , system (31) is unstable and a peri- (31) is stable in the region below the curves, but unstable above them odic solution occurs. The corresponding waveform and phase plane diagrams are shown in Fig.…”

“…In recent years, the stability analysis and the feedback control of time delay systems have been widely investigated since delays are often encountered in various engineering systems (see, i.e., [29][30][31][32][33][34][35]). On the other hand, descriptor systems with or without time delay have been extensively studied in recent years (see, i.e., [11,14,[17][18][19][20][21][22][23][24]27], and the references therein).…”

Stability and bifurcation analysis of Westwood+ TCP congestion control model in mobile cloud computing networks

“…However, how does TCP/AQM system evolves when the congestion control system loses its stability? This field also begins to draw much attention from researchers [4,5,6,10,11,12,13,14,20,21,25,26,27,28,29,32,33]. In [27], Raina et al found that if the local stability of TCP with drop tail is just lost, the corresponding nonlinear system undergoes a supercritical Hopf bifurcation.…”

“…In [4,5], Ding et al analyzed Hopf bifurcation in a fluid flow model and a dual model of Internet congestion control algorithm. Moreover, we studied stability and Hopf bifurcation analysis in a novel congestion control model with communication delay and heterogeneous delays in [10,11,14] and analyzed Hopf bifurcation in an exponential RED algorithm with communication delay and heterogeneous delays in [12,13]. Xu et al studied bifurcation analysis and control in exponential RED algorithm in [32].…”