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Fig. 4.
Reconstruction of potential
V
(
c
) for
p
2
= 0 (left) and for the kink dynamics
on the line
p
2
=1
− p
1
(right).
Fig. 5.
Case
H
=0,
J
=
−∞
: the mean field map Eq. (2) (left) for
r
= 10 and
q
=2
and the mean-field
r − q
phase diagram (right). In the phase diagram the absorbing
states are always present. Points mark parameter values for which the absorbing states
are the only stable attractors. A plus sign denotes period-2 temporal oscillations be-
tween absorbing states, a star denotes the presence of a stable point at
c
=0
.
5, a
cross (circle) denotes period-two (four) oscillations between two non-zero and non-one
densities, triangles denote chaotic oscillations.
where
P
(
c,t
) is the probability of observing a density
c
at time
t
. One possible
solution is a
δ
-peak centered at the origin, corresponding to the absorbing state.
By considering only those trajectories that do not enter the absorbing state
during the observation time, one can impose a detailed balance condition, whose
effective agreement with the actual probability distribution has to be checked
a
posteriori
. The
effective potential V
is defined as
V
(
c
)=
−
log(
P
(
c
)) and can be
found from the actual simulations.
In the left panel of Fig. 4 we show the profile of the reconstructed potential
V
for some values of
p
around the critical value on the line
p
2
= 0, over which
