  Equilibrium and nonequilibrium systems exhibit power-law singularities close
to their critical and bifurcation points respectively. A recent study has shown
that biochemical nonequilibrium models with positive feedback belong to the
universality class of the mean-field Ising model. Through a mapping between the
two systems, effective thermodynamic quantities like temperature, magnetic
field and order parameter can be expressed in terms of biochemical parameters.
In this paper, we demonstrate the equivalence using a simple deterministic
approach. As an illustration we consider a model of population dynamics
exhibiting the Allee effect for which we determine the exact phase diagram. We
further consider a two-variable model of positive feedback, the genetic toggle,
and discuss the conditions under which the model belongs to the mean-field
Ising universality class. In the biochemical models, the supercritical
pitchfork bifurcation point serves as the critical point. The dynamical
behaviour predicted by the two models is in qualitative agreement with
experimental observations and opens up the possibility of exploring critical
point phenomena in laboratory populations and synthetic biological circuits.
