Linear pattern dynamics in nonlinear threshold systems

Complex nonlinear threshold systems frequently show space-time behavior tha t is difficult to interpret. We describe a technique based upon a Karhunen- Loeve expansion that allows dynamical patterns to be understood as eigensta tes of suitably constructed correlation operators. The evolution of space-t ime patterns can then be viewed in terms of a "pattern dynamics" that can b e obtained directly from observable data. As an example, we apply our metho ds to a particular threshold system to forecast the evolution of patterns o f observed activity. Finally, we perform statistical tests to measure the q uality of the forecasts.