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Weakly Nonlinear Stability Analyses of Prototype Reaction-Diffusion Model Equations

Comparisons are made between the results obtained by the application of various methods of weakly nonlinear stability analysis to several prototype reaction-diffusion equations which among them reproduce most of the salient features representative of such investigations of model systems for dissipative phenomena. Emphasis is placed upon the subtleties involved in scaling these equations and deducing asymptotically valid solutions. Phenomenological interpretations of the bifurcation behavior of the model equations are offered, based on the pattern formational aspects of convective instabilities in hydrodynamics, morphological instabilities in solidification, and diffusive instabilities in ecology.