Analysis of an oscillatory kinetic mechanism, employing two surface concentrations with widely separated diffusivities as its dynamic variables, reveals that the apparent kinetics of a homogeneously exposed isolated catalyst may vary with its size due to emergence of asymmetric states. The rate curves, predicted by the model, pass through a maximum that is shifted to lower reactant concentrations with increasing catalyst length. The branch of the rate curve of inhomogeneous solutions may bifurcate from the homogeneous branch or may form an isola. The stability of the uniform and asymmetric solutions is considered. The rate curves predicted by the model and the length scales associated with it resemble some of the experimental observations of structure sensitivity, suggesting that the sensitivity of specific reaction rate to crystallite size may be induced by non-linear kinetics.