SYNERGETICS AND BIFURCATION THEORY *

Synergetics'-6 is a rather new field of interdisciplinary research related to mathematics, physics, astrophysics, electrical and mechanical engineering, chemistry, biology, ecology, and possibly to other disciplines. It studies the selforganized behavior of complex systems (composed of many subsystems) and focuses its attention to those phenomena where dramatic changes of macroscopic patterns or functions occur owing to the cooperation of subsystems. Some examples are exhibited in FIGURE 1. In spite of this rather general scope, synergetics has been able to unearth astounding analogies between entirely different systems. In the course of this research program it more and more transpired that bifurcation theory plays a crucial role. As long as the systems we are encountered with can be described by mathematical models we very often deal with the following problem. A system is represented by a set of time-dependent variables

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