Accuracy in qualitative description of behaviour

The author illustrates some aspects of the relationship between conventional and qualitative approaches to system dynamics. A simple second-order system is used to illustrate the use of qualitative methods, including a qualitative calculus. An extension to a nonlinear case is also shown. In both approaches (conventional and qualitative) there is a need for care in defining the model to be used and in understanding the limitations of the model and the corresponding impact on results. The relationship between conventional and qualitative results is important, because it touches on the issue of accuracy. There is no reason why qualitative reasoning per se should not be completely accurate, within the limits imposed by the relatively coarse resolution, and the examples presented show one way of achieving this. Qualitative vectors prove to be a convenient and expressive tool in representing system behaviors. They preserve and even reinforce the correspondence between conventional and qualitative mathematics