A Representative Example of Dissipative Structure

Abstract

The examples of dissipative structures in nature are too numerous to count. In most cases, in addition to the complexity arising from the nonlinear nature of the governing laws, there are various external factors whose combined influence causes the behavior to become even more complex. For this reason, it is very important in an attempt to understand dissipative behavior that we carefully select a few model examples from the multitude and concentrate our study on such examples by employing well-controlled conditions. In so doing, it becomes possible to apprehend the general features of dissipative structures that transcend the specific features of individual systems. In this sense, the examples discussed in this chapter, Bénard convection and the Belousov- Zhabotinskii reaction, are representative, and it is perhaps not inaccurate to state that the development seen in the research of nonlinear nonequilibrium systems in the context of chaos and dissipative structures has been made largely through the study of these two examples. In this chapter we discuss the prominent characteristics of the method used to study nonlinear nonequilibrium systems through the application of this method to these two specific problems. In so doing, we make several preliminary observations in preparation for later chapters.