Nonconstant Dynamic States and Their Bifurcations

The mathematical analysis of an evolution process requires as a starting point a reliable formulation of the relevant interactions (evolution equation, mathematical model). It thus implies a profound understanding of the internal mechanism of the evolution process, based on experimental observations and on previous experience. Otherwise such an analysis will hardly possess any significant predictive capability. It is noteworthy that the study of nonconstant steady states of natural processes requires a knowledge of the corresponding dynamic laws. Unfortunately, in system dynamics there are no universal laws, analogous to those of Newton in mechanics or those of Maxwell in electromagnetism. Moreover, the separation of a complex dynamic interaction into a disjoint, or loosely coupled set of more elementary interactions, is in general much more difficult in system dynamics than in physics or engineering. In spite of the absence of universal dynamic laws, there exist numerous particular cases for which a verbal description of the internal mechanism is available, which is adequate at least for a qualitative explanation of the observed time evolution. This verbal description, backed up by some typical evolution curves, permits not only the establishment of a mathematical model but also a transformation of the model into a form which accentuates certain features (deductive truisms) which are impossible or difficult to observe directly, that is, it facilitates a discrimination between plausible alternatives. A certain number of deductive truisms concerning nonconstant steady states are briefly described.