Stabilizing Turing patterns with subdiffusion in systems with low particle numbers.

The role of subdiffusion in the formation of spatial Turing patterns with particle number fluctuations is studied. It is demonstrated for a generic activator-inhibitor system that for normal diffusion the particle number fluctuations stabilize the homogenous steady state in a regime where the mean-field analysis already predicts stable spatial patterns. In contrast, pattern formation is stabilized considerably even for very low particle numbers when the activator moves subdiffusively while the inhibitor diffuses normally. In particular, this also holds true when the subdiffusive activator spreads faster than the inhibitor on small time scales. Possible applications to pattern formation in cell biology are discussed.