  We study the linear instabilities and bifurcations in the Selkov model for
glycolysis with diffusion. We show that this model has a zero wave-vector,
finite frequency Hopf bifurcation to a growing oscillatory but spatially
homogeneous state and a saddle-node bifurcation to a growing inhomogeneous
state with a steady pattern with a finite wavevector. We further demonstrate
that by tuning the relative diffusivity of the two concentrations, it is
possible to make both the instabilities to occur at the same point in the
parameter space, leading to an unusual type of codimension-two bifurcation. We
then show that in the vicinity of this bifurcation the initial conditions
decide whether a spatially uniform oscillatory or a spatially periodic steady
pattern emerges in the long time limit.
