HYPERBOLIC REACTION - DIFFUSION-EQUATIONS, PATTERNS, AND PHASE SPEEDSFOR THE BRUSSELATOR

In this paper, we study the hyperbolic reaction-diffusion equations fo r the irreversible Brusselator. We show that the phase speed of travel ing oscillating chemical waves can be obtained from the linearized hyp erbolic reaction-diffusion equations. The Luther-type speed formula is obtained in the lowest-order approximation. We also solve the hyperbo lic reaction-diffusion equations for two spatial dimensions and study the evolution of patterns formed. The patterns can evolve from a symme tric to a chaotic form as the reaction-diffusion number is varied. The two-dimensional power spectra of such chaotic-looking spatial. patter ns are shown still to preserve some symmetry in the two-dimensional re ciprocal space although the cross sections of the power spectra have t he signatures of chaotic patterns. It is interesting that even chaotic patterns have some sort of symmetry in the two-dimensional reciprocal space-Fourier space.