INSTABILITIES IN PROPAGATING REACTION-DIFFUSION FRONTS

Simple reaction-diffusion fronts are examined in one and two dimension s. In one-dimensional configurations, fronts arising from either quadr atic or cubic autocatalysis typically choose the minimum allowable vel ocity from an infinite spectrum of possible wave speeds. These speeds depend on both the diffusion coefficient of the autocatalytic species and the pseudo-first-order rate constant for the autocatalytic reactio n. In the mixed-order case, where both quadratic and cubic channels co ntribute, the wave speed depends on the rate constants for both channe ls, provided the cubic channel dominates. Wave propagation is complete ly determined by the quadratic contribution when it is more heavily we ighted. In two-dimensional configurations, with unequal diffusion coef ficients, the corresponding two-variable planar fronts may become unst able to perturbations. The instability occurs when the ratio of the di ffusion coefficient for the reactant to that for the autocatalyst exce eds some critical value. This critical value, in turn, depends on the relative weights of the quadratic and cubic contributions to the overa ll kinetics. The spatiotemporal form of the nonplanar wave in such sys tems depends on the width of the reaction zone, and a sequence showing Hopf, symmetry-breaking, and period-doubling bifurcations leading to chaotic behavior is observed as the width is increased.