INSTABILITIES OF FRONT PATTERNS IN REACTION DIFFUSION-SYSTEMS

Recent experiments in chemical reaction-diffusion systems with externally imposed concentration gradients may provide access to a host of spatio-temporal pattern formation phenomena. These systems tend to form steep reaction fronts in response to the external gradient. We use singular perturbation techniques, normal form calculations and numerical simulations to investigate the existence and the stability of such sustained fronts. In one-dimensional systems, the theoretical predictions are found in quantitative agreement with direct simulations of the Hopf bifurcation from steady to periodically oscillating front structures observed in the Couette flow reactor. Also conditions are found under which oscillations of the spatial structure become chaotic. In two-dimensional systems, we address the issue of realizing an experimental situation hitherto unattained: a one-dimensional chain of coupled oscillators at the onset of the Hopf destabilization of the front structure. We point out the intimate relationship between the frequency of oscillation, omega, of the homogeneous front pattern and the characteristic wavelength, lambda, of the Turing pattern that can develop along the front; lambda almost-equal-to 2-pi(D/omega)1/2. We comment on subsequent bifurcations that may result from the nonlinear interaction between Hopf and Turing instabilities as the precursors to spatio-temporal chaos. In conclusion, we emphasize the possibility of probing the transition to "mediated defect turbulence" in thin film gel reactors.