Igneous rocks very commonly show a strongly bimodal distribution of compositions, one mode corresponding to basalt and the other to felsic magmas(1-3). As fractional crystallization of basaltic parents produces a continuum of compositions, the paucity of rocks of intermediate composition-commonly called the Daly gap-has puzzled petrologists since the time of Daly. Gravitational or viscous trapping(4,5), large crystal loads restraining convection(6,7), and re-melting of deep volcanic layers(2) are among the processes that have been offered as physically meaningful explanations of magmatic gaps. Here we propose an alternative interpretation, transposed from chemical reactor control theory(8) : at large undercooling, thermal feedback in a continuously fed and differentiating magma reservoir promotes the existence of competing thermochemical steady states. Small variations in magma residence time and cooling rate induce a large thermal and chemical swing (magmatic bifurcation or catastrophe), which interrupts the liquid line of descent, leading to bimodal erupted products.