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

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

2007-12-22

arxiv.org/abs/0712.3831v1

Computer Science

Networking and Internet Architecture

18 pages, 6 figures

Scientific paper

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.

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