Patterns and their instabilities in catalytic carbon monoxide oxidation

This thesis deals with the computer assisted stability analysis of non-linear patterns in a model of CO oxidation on Pt(110). Experimentally this system has been shown to exhibit a rich variety of spatiotemporal concentration patterns which are modeled by reaction-diffusion equations.; We focus on the dynamics and instabilities of selected non-linear patterns. Since these patterns are nonlinear, a computational approach is necessary. The general approach is to study the dynamics of these patterns using numerical simulations and bifurcation analysis. The reaction-diffusion PDE is discretized in space, resulting in a large dimensional dynamical system. Appropriate dynamical systems tools are then employed to determine the stability of these patterns.; First, we consider the dynamics of solitary pulses travelling with constant speed in large periodic domains in 1-D. These pulses undergo a variety of instabilities ranging from oscillatory instabilities to the so-called “backfiring” instability. We perform a detailed analysis of the dynamics of these pulses as a function of two of the model parameters. This is achieved by studying this travelling pulse as a steady state in the co-moving frame. This results in a very complicated scenario of transitions and bifurcations of pulses in this two-parameter space. Next, we study travelling pulse-like structures in an annular domain where the diffusion of the species on the underlying substrate is anisotropic. This results in the shape and speed of the pulse changing from location to location. We perform a detailed study of the dynamics and instabilities of these pulses in the case when the annulus is thin. In this case, a reduction can be made to a one-dimensional system with position dependent diffusivity. Since the pulse no longer moves with constant speed, fully time-dependent calculations involving numerical Floquet analysis are performed. The effect of anisotropy on the pulse dynamics is systematically probed. These pulses, while inheriting some of the instabilities of pulses in homogeneous media, also possess instabilities which have no analog in the homogeneous case. Finally we briefly study some of the instabilities of target patterns via a one-dimensional model. Instabilities associated with both the discrete and continuous components of the spectrum are observed.