Patterns due to quintic kinetics in a diffusion-reaction system with global interaction

Abstract

We study the process of pattern selection in a catalytic ribbon or disk subject to global interaction. The diffusion-reaction system, xt−Δx=f(x,y)−〈f(x,y)〉; yt=ε(−αx−y), with a quintic source function f(x,y)=−x(x2−1)(x2−a2)+y, qualitatively describes the behavior of catalytic or electrochemical oscillations subject to control or gas-phase mixing and the kinetics describes a system with two simultaneous or consecutive reactions. This model shows a richer class of solutions than the extensively studied one with a cubic source function (f=−x3+x+y) since f(x)=0 is tristable and for a wide separation of time scales the system admits, without global interaction, coexistence of a stable and oscillatory states. Also the reaction-diffusion equation with a quintic source may admit one large and two small fronts and their domains of existence and stability are mapped. Under global interaction the system exhibits all the patterns unveiled with the “cubic kinetics,” along with multifront patterns and new patterns at the border of instability of the large front.