Hopf bifurcation analysis in a dual model of Internet congestion control algorithm with communication delay

TL;DR

This paper analyzes how communication delays induce Hopf bifurcations in a dual Internet congestion control model, identifying critical delays and characterizing resulting oscillations through theoretical and numerical methods.

Contribution

It provides a detailed analysis of delay-induced Hopf bifurcations in a dual congestion control model using delay differential equations and perturbation techniques.

Findings

Hopf bifurcation occurs at a critical communication delay value.

Periodic solutions emerge and their stability is characterized.

Numerical simulations confirm theoretical predictions.

Abstract

This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing communication delay as the bifurcation parameter, we demonstrate that the system loses its stability and a Hopf bifurcation occurs when communication delay passes through a critical value. Moreover, the bifurcating periodic solution of system is calculated by means of perturbation methods. Discussion of stability of the periodic solutions involves the computation of Floquet exponents by considering the corresponding Poincare -Lindstedt series expansion. Finally, numerical simulations for verify the theoretical analysis are provided.