Today neural networks are being adopted as an alternate method of solving complex pattern recognition/classification problems. Information regarding performance measure is critical in evaluating the capacity of this system in performing recognition/classification tasks. Currently this information is obtained using unstandardized empirical techniques. This study will attempt to devise a methodical procedure to qualitatively predict the performance measure of all neural network recongition classification systems governed by a set of ordinary differential equations. The determination of this characteristic will be made through the use of specific analytic methods in mathematics. Dynamical systems can therefore be qualitatively analyzed, and issues regarding existence of parasitic limit points can be more effectively addressed.