SPATIOTEMPORAL MOTIONS DUE TO GLOBAL INTERACTION

The global interaction between the spatial average of the autocatalytic variable in a reactive (catalytic, electrochemical, gel) medium and a surrounding mixed fluid in a continuously fed vessel may induce a rich structure of spatiotemporal patterns that would not exist otherwise. Patterns may form when the local kinetics are either excitable, oscillatory, or bistable and the reaction rate ascends with reactant concentration. Thus, a local change in the surface reaction rate may affect the reactant concentration in the surrounding well-mixed vessel, so that it arrests moving fronts on the surface. External control of the average temperature (or rate) of a catalytic ribbon by electrical heating is another form of interaction between a spatial average of a local oscillator and a space-independent variable that induces pattern formation. We study various patterns and bifurcations that can develop in a ring or a ribbon due to global interaction using a simple cubic kinetic expression. The predominant pattern on a catalytic ring is a rotating pulse. Other patterns, such as antiphase oscillations and crossing pulses, similar to those found previously on a controlled catalytic ribbon, may coexist for a sufficiently strong interaction. Several of the transitions between regions with qualitatively different patterns are via global bifurcation.