PATTERN-FORMATION IN A CUBIC AUTOCATALATOR MODEL - THE EFFECT OF THE UNCATALYZED REACTION

The bifurcation from the uniform state to non-homogeneous solutions, e ither steady patterns or time-dependent standing waves, is considered in a reaction-diffusion system based on the cubic autocatalator kineti cs with the extra uncatalyzed reaction producing the autocatalyst B di rectly from reactant A included. It is shown that if this extra reacti on step is sufficiently strong, the uniform state is stable to all per turbations (i.e. for r>1/8, where r is a measure of the strength of th is step). For r(0) = 1/64(71 - 17 root 17) < r < 1/8 bifurcations to t ime-dependent standing waves are possible, and for 0 < r < r(0), bifur cations to steady non-homogeneous solutions are also possible. These n on-homogeneous solutions are followed from their bifurcation points by a spectral method.