Pattern formation and chemical evolution in extended Gray-Scott models

Abstract

Pattern formation in reaction-diffusion systems has been the subject of study in a variety of natural disciplines. In this thesis we investigate the behaviour of an abstract pattern-forming autocatalytic system based on the Gray-Scott model, featuring a small number of related chemical species. The aim is to investigate the form of interaction that takes place between these species, whether competition or cooperation, and how this relates to the overall pattern generation. Through the perspective of chemical evolution we seek to observe what long-term behaviour emerges, both in terms of population composition and structure formation. The work is largely exploratory and we approached the observed system properties from various angles to characterise them. We report that systems composed of 2 species were seen to be unstable and only achieve transient joint pattern formation, while the 3-species extension reached stability for a limited class of configurations. This class produced rich behaviour in the form of dynamic patterns with shifting structural features involving long transients, including a novel type of pattern, not seen in other studies of the Gray-Scott model or related models. Both systems are examples of catalytic hypercycles. In terms of pattern formation, the exhibited structural features reflect local species populations and in general are not themselves decisive for the outcome of species interactions. In an unconstrained evolution scenario, we report a strongly directed evolutionary path towards selfish species and loss of structure.