Local Hopf bifurcation and global existence of periodic solutions in TCP system

Xu, Changjin; Tang, Xianhua; Liao, Maoxin

doi:10.1007/s10483-010-1312-x

Cited by 6 publications

(3 citation statements)

References 9 publications

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“…Hopf bifurcation refers to the phenomenon of periodic motion that arises from the equilibrium state when the bifurcation parameters cross the bifurcation point. In order to distinguish the type of Hopf bifurcation in the landing gear system, this section utilizes canonical theory to derive the discriminant for identifying the type of Hopf bifurcation in the landing gear system [24].…”

Section: Analysis Of the Time-delay Effect Under Linear Dampingmentioning

confidence: 99%

Research on the Stability and Bifurcation Characteristics of a Landing Gear Shimming Dynamics System

Ruan,

Zhang,

Yang

et al. 2024

Aerospace

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A dynamic model is established to investigate the shimmy instability of a landing gear system, considering the influence of nonlinear damping. The stability criterion is utilized to determine the critical speed at which the landing gear system becomes unstable. The central manifold theorem and canonical method are employed to simplify the dynamic model of the landing gear. The first Lyapunov coefficient of the system is theoretically derived and verified using numerical simulation. Further investigation on the Hopf bifurcation characteristics and stability of the shimmy in the landing gear system is conducted. The results indicate that above a certain threshold speed, with a tire stability distance greater than half the tire length in contact with the ground plus the slack length, the aircraft remains stable during taxiing. At critical speeds, a shimmy system with higher-order nonlinear damping will undergo supercritical Hopf bifurcation. Quantitative analysis suggests an increase in the linear damping coefficient within a range that ensures a stability margin to mitigate undesired oscillation, while the nonlinear damping coefficient should be designed within a reasonable range to decrease the amplitude of the limit cycle.

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Section: Analysis Of the Time-delay Effect Under Linear Dampingmentioning

confidence: 99%

Research on the Stability and Bifurcation Characteristics of a Landing Gear Shimming Dynamics System

Ruan,

Zhang,

Yang

et al. 2024

Aerospace

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“…Over the past years, many internet congestion control mechanisms have been developed to ensure the reliable and efficient exchange of information across the internet, such as Active Queue Management (AQM). Bifurcation analysis of TCP under various congestion control mechanisms have been studied by several authors [16,25,30,32,40,41]. All have used a continuous-time model (e.g., the fluid model) and applied traditional mathematical methods of bifurcation analysis, including simulations, to detect parameter values when the system passes through a critical point, the system loses its stability, and a so-called Hopf bifurcation occurs [22].…”

Section: Introductionmentioning

confidence: 99%

Digital Bifurcation Analysis of TCP Dynamics

Beneš

Brim

Pastva

et al. 2019

Tools and Algorithms for the Construction and Analysis of Systems

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Digital bifurcation analysis is a new algorithmic method for exploring how the behaviour of a parameter-dependent computer system varies with a change in its parameters and, in particular, for identification of bifurcation points where such variation becomes dramatic. We have developed the method in an analogy with the traditional bifurcation theory and have it successfully applied to models taken from systems biology. In this case study paper, we demonstrate the appropriateness and usefulness of the digital bifurcation analysis as a push-button alternative to the classical approaches as traditionally used for analysing the stability of TCP/IP protocols. We consider two typical examples (congestion control and buffer sizes throughput influence) and show that the method provides the same results as obtained with classical non-automatic analytical and numerical methods.

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“…Hollot et al [25] and Misra [26] formulated the mathematical model of TCP/AQM using stochastic differential equations and studied the stability of the equilibrium of the model. Such a model includes the maximum amount of the technical details of the congestion control algorithm, and therefore attracts much attention from the researchers [27][28][29][30][31] . However, due to the same reason, the model is highly complicated for further analysis from the theoretical perspective.…”

Section: Introductionmentioning

confidence: 99%

Suppression of oscillatory congestion via trunk link bandwidth and control gain in star network

Shu

Wang

2018

Appl. Math. Mech.-Engl. Ed.

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The time delay-induced instability in an Internet congestion control model is investigated. The star topology is considered, and the link bandwidth ratio and the control gain are selected as the tunable parameters for congestion suppression. The stability switch boundary is obtained by the eigenvalue analysis for the linearized system around the equilibrium. To investigate the oscillatory congestion when the equilibrium becomes unstable, the center manifold reduction and the normal form theory are used to study the periodic oscillation induced by the delay. The theoretical analysis and numerical simulation show that the ratio between bandwidths of the trunk link and the regular link, rather than these bandwidths themselves, is crucial for the stability of the congestion control system. The present results demonstrate that it is not always effective to increase the link bandwidth ratio for stabilizing the system, and for some certain delays, adjusting the control gain is more efficient.

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Local Hopf bifurcation and global existence of periodic solutions in TCP system

Cited by 6 publications

References 9 publications

Research on the Stability and Bifurcation Characteristics of a Landing Gear Shimming Dynamics System

Research on the Stability and Bifurcation Characteristics of a Landing Gear Shimming Dynamics System

Digital Bifurcation Analysis of TCP Dynamics

Suppression of oscillatory congestion via trunk link bandwidth and control gain in star network

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