Turing patterns under a periodically forced feed

Alan Turing proposed one of the most influential theories of morphogenesis, in which a system of diffusive and reactive chemicals can produce stationary (and other types) spatial patterns. We explored the effect of periodic feeding of the reactive chemicals on pattern development and stabilty.

The periodic change of parameters we applied in this work is common in natural biological systems, where parameters having various periods (diurnal, seasonal, yearly) dictated by the environment and biochemical cycle of the organisms. These parameter changes are much more significant than the effect of fluctuations against which the Turing systems are stable.  

The first experimental realization of Turing patterns  was made in 1991 by the group of Patrick De Kepper in Bordeaux, which made it possible to study many different aspects of this phenomenon. Here we studied the effect of a sinusoidal modulation of the inflow rate of one of the reagents in a chemical reaction-diffusion system capable of producing Turing patterns. We found experimentally that periodic forcing can destabilize the pattern developed at a constant inflow rate and generate stationary patterns from the no-pattern regime. To support our experimental observations, we performed numerical simulations and semi-analytic linear stability analyses of the system. 

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