ABSTRACT
In general, the method of analysis applied to any nonlinear system depends to a large extent on the structure of the model representation. The combination of qualitative and numerical techniques has provided a useful, and more importantly flexible, methodology for the analysis of nonlinear systems. In control studies, the augmentation of the system model with one or more parameters enables the study of the system’s behavior over a specified range of parameter values. The stability of a model, both absolute and structural, is dependent on the location and distribution of degenerate singularities on the solution manifold of that system. The advantage of the parameterized cell map approach is that it combines the qualitative aspects of dynamical systems theory with the global aspect afforded by the unraveling algorithm. The dynamical systems approach is attractive in that it provides information on the very type of qualitative behavior the nonlinear model was constructed to emulate.
