Authors:   Marko Hofmann, Thomas Krieger

Abstract

In many complex systems a small change of the independent variables X (input) may completely change the value of the dependent variable Y (output). We call this behavior erratic and try first to find a formal definition for it. Erratic behavior can also be reproduced in corresponding simulation systems. By calibration it is even possible fine-tune the simulation to the real world data, achieving high descriptive validity. However, since the real system is highly sensitive to minor changes of the initial conditions, the simulation model must reach an equally high level of fidelity if ti comes to prediction. Even a qualitatively appropriate forecast could be of low value if the erratic behavior leads to high quantitative deviations. Unfortunately, the fidelity of simulation models is limited by many factors including available system data, money, and time. Thus, the initial conditions of the real system can only be approximated in the model input. Modeling necessarily introduces a certain amount of uncertainty with respect to the real world situation. Consequently, a tolerable level of deviation has to be defined which might be easily exceeded in the case of erratic behavior. Based on two examples we generalize this problem and try to systemize its investigation on the basis of some preliminary formal definitions. The ultimate goal of this research endeavor is the ability to assess the power of simulation-based predictions with respect to the future behavior of systems that have shown erratic behavior in the past.