THRESHOLD BIFURCATION IN TISSUE INTERACTION MODELS FOR SPATIAL PATTERN GENERATION

Experimental evidence indicates that tissue interaction plays an essen tial role during skin pattern formation. Here we focus on the mathemat ical aspects of two specific tissue interaction models. Introducing in teraction mechanisms into the traditional pattern formation models is not only biologically consistent, but also leads to results agreeing m ore closer to those observed in embryogenesis. We specifically examine the bifurcations from spatially simple solutions to spatially complex patterns. In both models this increased complexity in solution is obt ained by increasing the effect of the interaction mechanism through a certain threshold. The role of tissue interaction in sequential patter ning is also considered.