Title: Chaos You Can Play In
Authors: Aaron Clauset, Nicky Grigg, May Lim, Erin Miller
Introduction
Real world instances of complex systems often exhibit complex
dynamical behavior that is not well characterized as either periodic
or random. Indeed, many such systems exhibit chaotic or quasiperiodic
behavior. Systems which exhibit chaotic dynamics may be broken
into mathematical models, many of which like the logistic map
or the Lorenz equations are well understood, and real world systems.
Chaos in real world systems is significantly more difficult to
both model mathematically and explore experimentally. This is
due not only to the inherent variability which chaotic behavior
creates, but also the inherent difficulties in acquiring good
time series measurements. Noise and low sampling rates present
problems, as does the fact that there may only be a single stream
of data that can be measured in a real system, while in a mathematical
model, all variables of interest can be analysed.
Willem Malkus and Lou Howard Strogatz in the 1970s
at MIT improvised the waterwheel, a mechanical analogue of the
Lorenz equations. Surprisingly, the waterwheel has remained a
largely unexplored system, with what little work has been done
focusing on simplifications of the mathematical model. The beauty
of the waterwheel is in its simplicity. Water is poured into the
system at a steady rate from the top of the tilted wheel. Each
cup has a hole drilled in the bottom which allows water to leak
out of the system. Some damping is introduced into the rotation
of the wheel. By varying only two parameters, the inflow rate
of water and friction applied to the wheel, one can cause the
wheel to exhibit simple periodic behavior (either unidirectional
behavior where the wheel rotates continuously in one direction,
or bidirectional behavior in which the wheel reverses direction
periodically) or unpredictable transitions between these two simple
behaviors. In this paper we describe an experimental and modeling
study of the Malkus waterwheel system.
"Chaos
You Can Play In" published in the SFI CSSS 2003 proceedings

