  Chaotic behavior can be produced from difference equations with unstable
fixed points. Difference equations can be used for algorithms to control the
chaotic behavior by perturbing a system parameter using feedback based on the
first difference of the system value. This results in a system of nonlinear
first order difference equations whose stable fixed point is the controlled
chaotic behavior. Basing the feedback on the first difference produces
distinctly different transient responses than when basing feedback on the error
from the fixed point. Analog electronic circuits provide the experimental
system for testing the chaos control algorithm. The circuits are low-cost,
relatively easy to construct, and therefore provide a useful transition towards
more specialized real-world applications. Here we present predictions and
experimental results for the transient responses of a first difference based
feedback control method applied to a chaotic finite difference 1-dimensional
map. The experimental results are in good agreement with predictions, showing a
variety of behaviors for the transient response, including erratic appearing
non-steady convergence.
