Bifurcations and Chaos in a Periodically probed Computer Network

In this paper we model a computer network consisting of one standard Internet connection and one nonstandard connection that transmits uniformly sized bursts of packets at regular intervals. The nonstandard connection can represent probing activity of either a diagnostic measurement or attack. Using bifurcation diagrams, we study how the network’s behavior changes as a function of the probing frequency. These diagrams reveal interesting, nonintuitive behavior. We present a series of models of increasing simplicity that capture the significant features of the network’s behavior. Our simplest model is a piecewise linear, discontinuous one-dimensional map. This map helps explain the structure of the bifurcation diagram, and allows us to directly determine Lyapunov exponents, which give a measure of the system’s predictability. As a result, we are able to more precisely describe and categorize the dynamics, including chaos, exhibited by this network.