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Next: Self-similarity. Up: RESULTS ON CHAOTIC Previous: States and state

Typical behaviour.

In this section, we concentrate on a selection of results from computer experiments on a network.

Diagrams will be shown which illustrate throughput load characteristics for the system, the overall average packet age over a run of 20,000 token passes versus percentage load, and the average number of packets arriving at their destination, per token pass, as the load is varied.

We now look at the behaviour of the average age as a function of discrete time i. Only in exceptional circumstances does display periodic behaviour with a short period --- typically when the load is very low (one or two packets) or high (almost fully loaded). For intermediate values of load, apparently aperiodic behaviour is always observed. Several average age waveforms will be shown for different values of load. The initial transient is not shown. Despite the fact that the system is deterministic, these waveforms have a surprisingly noise-like appearance.

There is evidence [4] that chaotic behaviour is displayed by the network, based on a numerical computation of Lyapunov exponents [3]. These are a measure of exponential divergence of initially close state vectors, as defined above, and a positive Lyapunov exponent is a strong indicator of the presence of chaotic behaviour.



D Jefferies
Mon May 27 11:45:34 BST 1996