Period Doubling, Border Collision and Slowly Oscillating Periodic  Orbits (SOP) in Internet Protocol Dynamics

Priya Ranjan, University of Maryland, College Park  & Intelligent Automation Inc.

In this talk a novel nonlinear invariant theory based
(in)stability results for  optimal rate allocation schemes will be
presented. We will characterize the stability conditions with an
arbitrary fixed communication delay in the context of optimization
framework for the rate allocation problem proposed by Kelly.

New results about this system behavior after it loses stability will
also be presented.

Various generalizations like presence of time varying delay,  distributed
delay, feedback based on averaging, stochastic stability will be  derived
in the invariance framework along with illustration of smooth and
non-smmoth bifurcations and Slowly Oscillating Periodic Orbits (SOP).