Cluster compartmentalization may provide resistance to parasites for catalytic networks

We have performed calculations on reaction-diffusion equations with an aim to study two-dimensional spatial patterns. The systems explicitly studied are three different catalytic networks: a 4-component network displaying chaotic dynamics, a 5-component hypercycle network and a simple 1-component system. We have obtained cluster states for all these networks, and in all cases the clusters have the ability to divide. This contradicts recent conclusions that only systems with chaotic dynamics may give cluster states. On the contrary, we think that any network architecture may display cluster formation and cluster division. Our conclusion is in agreement with experimental results reported for an inorganic system corresponding to the simple 1-component system studied in this paper. In a partial differential equations model, the clusters do not provide resistance to parasites, which are assumed to arise by mutations. Parasites may spread from one cluster to another, and eventually kill all clusters. However, by combining the partial differential equations with a suitable cut-off rule, we demonstrate a system of partly isolated clusters that is resistant against parasites. The parasites do not infect all clusters, and when the infected clusters have decayed, they are replaced by new ones, as neighbouring clusters divide.