  The work reported here aims to address the effects of time-dependent
parameters and stochasticity on decision-making in biological systems. We
achieve this by extending previous studies that resorted to simple normal
forms. Yet, we focus primarily on the issue of the system's sensitivity to
initial conditions in the presence of different noise distributions. In
addition, we assess the impact of two-way sweeping through the critical region
of a canonical Pitchfork bifurcation with a constant external asymmetry. The
parallel with decision-making in bio-circuits is performed on this simple
system since it is equivalent in its available states and dynamics to more
complex genetic circuits. Overall, we verify that rate-dependent effects are
specific to particular initial conditions. Information processing for each
starting state is affected by the balance between sweeping speed through
critical regions, and the type of fluctuations added. For a heavy-tail noise,
forward-reverse dynamic bifurcations are more efficient in processing the
information contained in external signals, when compared to the system relying
on escape dynamics, if it starts at an attractor not favoured by the asymmetry
and, in conjunction, if the sweeping amplitude is large.
