Delay induced Hopf bifurcation in a dual model of Internet congestion control algorithm

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 [29], the delay induced Hopf bifurcation was studied in a simplified network congestion control model. 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].…”

Oscillation control for n-dimensional congestion control model via time-varying delay

“…The answer to this question is related to the nonlinear dynamics of the congestion control model. Therefore, in recent years, there has been a rapidly growing interest in the nonlinear dynamical behavior of congestion control model, such as bifurcations and chaos [8][9][10][11][12][13][14]. For example, in ref.…”

Stability and Hopf bifurcation of a class of TCP/AQM networks

“…(4), the direction, stability of the Hopf bifurcation was investigated by using the normal form theory and the center manifold theorem in [12], with which the DDE is converted into an operator equation on a Banach space of infinite dimension and then it is simplified into two-dimensional ordinary differential equations on the center manifold, a routine that requires a long tedious calculation. From the viewpoint of computation, the singular perturbation methods afford much simpler procedures that yield an excellent approximate solution for the bifurcated oscillation [13][14][15][16][17][18][19][20]. The method of multiple scales (MMS) is particularly preferable in applications, because it involves much easier computation than the center manifold reduction but gives the same results as the center manifold reduction does [15].…”

“…There is R * ∈ (0, R 0 ) such that α(R * ) = min{α(R)|R ∈ (0, R 0 )}. (20) In fact, assume that 0 < R = ε 1, then ω = o(ε) ≈ 0 as shown above, and…”