Transient Turing patterns in a morphogenetic model

One of the most surprising mechanisms to explain symmetry breaking phenomenon linked pattern formation is known as Turing instabilities. These patterns are self-organising spatial structures resulting from interaction at least two diffusive species in specific conditions. The ideas have been used extensively specialised literature both developmental patterns, well synthetic biology design. In present work we study a previously proposed morphogenetic circuit consisting genes controlled by same regulatory system. homogeneous version this simple model presents rich phase diagram, since it has saddle-node bifurcation, spirals and limit cycle. Linear stability analysis numerical simulations complete allow us determine conditions for development transient patterns. We found that parameter region where much smaller than occur. observed temporal evolution towards can one or different length scales, depending on initial Further, persistence time depends distance between parameters values which system operating boundary This singularity critical gives place metastable To best our knowledge, associated with instabilities not reported models.