Appearance and suppression of Turing patterns under a periodically forced feed

Abstract

Turing instability is a general and straightforward mechanism of pattern formation in reaction–diffusion systems, and its relevance has been demonstrated in different biological phenomena. Still, there are many open questions, especially on the robustness of the Turing mechanism. Robust patterns must survive some variation in the environmental conditions. Experiments on pattern formation using chemical systems have shown many reaction–diffusion patterns and serve as relatively simple test tools to study general aspects of these phenomena. Here, we present a study of sinusoidal variation of the input feed concentrations on chemical Turing patterns. Our experimental, numerical and theoretical analysis demonstrates that patterns may appear even at significant amplitude variation of the input feed concentrations. Furthermore, using time-dependent feeding opens a way to control pattern formation. The patterns settled at constant feed may disappear, or new patterns may appear from a homogeneous steady state due to the periodic forcing.