Turing instability in sub-diffusive reaction-diffusion systems

Linear stability characteristics of an anomalous sub-diffusive activator inhibitor system are investigated through a mesoscopic model, where anomaly ensues by a memory integro-differential operator with an equal anomaly exponent for all species. It is shown that monotonic instability, known from normal diffusion, persists in the anomalous system, thereby allowing Turing pattern occurrence. Presence of anomaly stabilizes the system by diminution of the range of diffusion coefficients' ratio involving instability. In addition, the maximal growth rate is diminished, proving the existence of an absolutely stable anomalous system.