IntroductionC omplexity abounds in chemically and biologically reacting systems: concentration waves and other complicated timevarying patterns form on the surface of a single crystal catalyst under isothermal, ultra-high vacuum conditions and patterns of concentrations and electrical potential occur in electrochemical reactions; neurons interact through the transmission of electrical and chemical signals; spiral waves and turbulent concentration motion occur in cardiac tissue; and complex calcium waves including spirals form in frog oocytes. To chemical engineers, this may be hardly surprising: in many traditional examples, such as a fixedbed reactor, concentrations and temperature vary throughout the bed and change with time. In some other fields, however, the importance of spatiotemporal dynamics is more recent news.Each of the above examples is a complex system made up of a number of coupled interacting, nonlinear processes. Over a period of years beginning in the 1950s sophisticated contributions of many groups appeared on the nonlinear behavior obtainable in a stirred open reactor (the CSTR) and on the bifurcation structure leading to multiple steady states and oscillations (Aris and Amundson, 1958). This reactor type was subsequently used to show the existence, characterization, and control of chaotic behavior in chemical systems.In chemically reacting systems the reaction rate is typically a function of both space and time, and greater complexities set in when spatial variations are allowed. We discuss in this perspective the spatiotemporal patterns that occur in dissipative distributed chemically reacting systems, how the interaction of nonlinear reaction and coupling among reaction sites determines structure, and how such structure can be controlled and engineered through external signals (pacemakers), feedback, and patterned catalytic structure.
Spontaneous and Engineered Pattern FormationThe degree of interaction among reacting sites is influenced both by the local reaction rate and the range and strength of the coupling. The synchronization theories of Winfree and Kuramoto on the emergence of coherence as coupling is imposed have played a fundamental role in the development of the field of nonlinear science dealing with collective dynamics (Winfree, 1980;Kuramoto, 1984). Even weak coupling can produce significant changes in the collective, or overall, behavior of a system. Strong interactions produce not only spatial patterns, but also changes of the dynamics of the individual sites. A classic example of the change in local dynamics through interactions is diffusion induced chemical turbulence in which local coupling of periodic oscillators produces chaos.In chemically reacting systems both the local and overall reaction rates can be influenced by synchronization of reaction sites. Other engineering applications of synchronization include microwave communications, high-power laser devices, and superconducting electronic systems. Visual and audio interactions make crickets chirp, fireflies flash, and ...