Stability and bifurcation analysis in a FAST TCP model with feedback delay

Zhan, Zhongwen; Zhu, Jie; Li, Wei

doi:10.1007/s11071-012-0450-y

Cited by 10 publications

(11 citation statements)

References 23 publications

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“…Lemma 1 (see [1]). Theorem 2 (see [10]). For system (2), one knows that the equilibrium point is asymptotically stable when > 0 and is unstable when 0 < < 0 .…”

Section: Hopf Bifurcation In Fast Tcp and Red Modelmentioning

confidence: 99%

“…In this section, we show the main results of Hopf bifurcation for the FAST TCP model in [10]. The model can be described by the following nonlinear differential equations:…”

Section: Hopf Bifurcation In Fast Tcp and Red Modelmentioning

confidence: 99%

“…In this section, we add three control methods to the original model [10] for postponing the Hopf bifurcation in FAST TCP model of the Internet congestion control system. First, we give state feedback control model: hybrid control model:…”

Section: Hopf Bifurcation In Controlled Systemmentioning

confidence: 99%

“…In [7], inherently inputto-state stability as well as globally asymptomatic stability without any specific conditions on the tuning parameter or update gain for FAST TCP operation has been proved by Razumikhin-type nonlinear small gain theorem. In [8][9][10], authors show sufficient conditions for the global asymptotic stability of FAST TCP in a single-link single-source network and multiple-link network with feedback delays. Then, stability criterion for double time-delay FAST TCP systems has proved the local asymptotical stability with the existence of delay when the round trip propagation delay is smaller than the queuing delay [11].…”

Section: Introductionmentioning

confidence: 99%

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Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes

Ding

Wang

Ding

et al. 2016

Journal of Control Science and Engineering

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We focus on the Hopf bifurcation control problem of a FAST TCP model with RED gateway. The system gain parameter is chosen as the bifurcation parameter, and the stable region and stability condition of the congestion control model are given by use of the linear stability analysis. When the system gain passes through a critical value, the system loses the stability and Hopf bifurcation occurs. Considering the negative influence caused by Hopf bifurcation, we apply state feedback controller, hybrid controller, and time-delay feedback controller to postpone the onset of undesirable Hopf bifurcation. Numerical simulations show that the hybrid controller is the most sensitive method to delay the Hopf bifurcation with identical parameter conditions. However, nonlinear state feedback control and time-delay feedback control schemes have larger control parameter range in the Internet congestion control system with FAST TCP and RED gateway. Therefore, we can choose proper control method based on practical situation including unknown conditions or parameter requirements. This paper plays an important role in setting guiding system parameters for controlling the FAST TCP and RED model.

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“…Lemma 1 (see [1]). Theorem 2 (see [10]). For system (2), one knows that the equilibrium point is asymptotically stable when > 0 and is unstable when 0 < < 0 .…”

Section: Hopf Bifurcation In Fast Tcp and Red Modelmentioning

confidence: 99%

“…In this section, we show the main results of Hopf bifurcation for the FAST TCP model in [10]. The model can be described by the following nonlinear differential equations:…”

Section: Hopf Bifurcation In Fast Tcp and Red Modelmentioning

confidence: 99%

Section: Hopf Bifurcation In Controlled Systemmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Hopf Bifurcation Control in a FAST TCP and RED Model via Multiple Control Schemes

Ding

Wang

Ding

et al. 2016

Journal of Control Science and Engineering

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“…16d makes it faster to reach the limit point in the phase space. [53][54][55][56][57], detailed processes of linear stability analysis are given out.…”

Section: Effect Of Cef On Hopf Bifurcationmentioning

confidence: 99%

Suppression of Hopf bifurcation in metal cutting by extrusion machining

et al. 2016

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Hopf bifurcation is a common phenomenon during the metal cutting process, which results in poor surface finish of the workpiece and inhomogeneous grain structure in materials. Therefore, understanding and controlling Hopf bifurcation in metal cutting are necessary. In this work, the systematic low-speed extrusion machining experiments were conducted to suppress Hopf bifurcation phenomenon. It is found that the suppression of Hopf bifurcation is achieved with the increasing constraint extrusion degree. In order to reveal the mechanism of the suppression of Hopf bifurcation, a new nonlinear dynamic model for extrusion machining is developed where the convection, the diffusion, the extrusion of constraint, the thermal-softening deformation and the fracture-type damage are included. the present theoretical model is effective to characterize the suppression of Hopf bifurcation in metal cutting. Based on the numerical calculation of the theoretical model, the mechanisms underlying in extrusion machining are further revealed: Fracture-type deformation is more important than the thermal-softeningtype deformation in low-speed extrusion machining; however, the thermal-softening-type deformation is the primary deformation mode for high-speed extrusion machining.

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