Turing-type instabilities in bulk–surface reaction–diffusion systems

In this contribution we consider a coupled bulk–surface reaction–diffusion system and for infinitely fast bulk diffusion its formal reduction to a non-local surface PDE model. Thereby, we review results of linear stability analyses for both models showing that Turing-type instabilities can occur for equal lateral diffusion coefficients. The stability results are confirmed by new numerical results. As a specific application, we study a model for a spatial and reaction cycle of signalling molecules in a cell.