Bifurcation analysis and control in exponential RED algorithm

Time effect on the dynamical behavior of a life energy system dynamic model

“…From an ecological viewpoint, the interaction parameter areas of coexistence for two components are desirable. This method is important for understanding the regulatory chemical mechanisms of ecological systems, which provides a control mechanism to ensure a coexistence transition from an equilibrium to a periodic oscillation with desired amplitude and robust period [2,5,15,16,22,23,26]. In addition, we would like to point out that we can also investigate the Hopf bifurcation of system (1.3) by choosing the delay τ 2 as bifurcation parameter.…”

Stability switches and Hopf bifurcations of an isolated population model with delay-dependent parameters

“…(4) Although much progress on the stability and Hopf bifurcation has been seen in various models with delay-independent parameters [31][32][33][34][35], a crucial point is that the dynamics of the systems differs dramatically if the corresponding characteristic equations involve the delay-dependent or the delay-independent coefficients. Most existing methods for studying the nonlinear dynamics fail when applied to the models with delay-dependent parameters.…”

“…For system (33), if the τ 2 Re( dλ dτ )| τ =τ 0 > 0(< 0), then the bifurcation periodic solutions near τ 0 are asymptotically stable (unstable) and the Hopf bifurcation is supercritical (subcritical).…”

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.…”

“…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]. More recently, Dong et al analyzed dynamics of a congestion control model in a wireless access network [6].…”