  A reaction-diffusion system exhibiting Turing's diffusion driven instability
is considered. The equation for an activator is supplemented by unilateral
terms of the type $s_{-}(x)u^{-}$, $s_{+}(x)u^{+}$ describing sources and sinks
active only if the concentration decreases below and increases above,
respectively, the value of the basic spatially constant solution which is
shifted to zero. We show that the domain of diffusion parameters in which
spatially non-homogeneous stationary solutions can bifurcate from that constant
solution is smaller than in the classical case without unilateral terms. It is
a dual information to previous results stating that analogous terms in the
equation for an inhibitor imply the existence of bifurcation points even in
diffusion parameters for which bifurcation is excluded without unilateral
sources. The case of mixed (Dirichlet-Neumann) boundary conditions as well as
that of pure Neumann conditions is described.
