Pattern selection in controlled reaction–diffusion systems

Abstract

When a chemical reaction is carried out on a catalytic ribbon, the spatial average temperature of which is kept constant by electrical heating, spatiotemporal temperature patterns form when the uniform steady state is unstable at the set temperature. Numerical simulations reveal periodic and aperiodic patterns of moving pulses, ‘‘breathing’’ pulses, or stationary and oscillatory fronts. The transitions between some of these patterns are intricate and proceed via global bifurcations. Bifurcation maps of parameter regions leading to specific patterns are used to gain insight into pattern formation and organization of these parameter regions. The relations among the dynamics of the uncontrolled system, the ribbon length, and the selected pattern are discussed. Similar patterns are expected to evolve in other reaction–diffusion systems subject to control of space-averaged properties.