To follow the evolution of the system dynamics,
iterations are performed
with added Gaussian noise, 
, having zero mean value,
and standard deviation 
such that at each iteration, the state variable is
For the main mapping (not the feature),
the added noise may possibly take the state variable outside
the range (0,1).
So if 
we set the state variable as
and if
we set the state variable as 
. This procedure is
equivalent to reflecting the mapping at the 0 and 1 boundaries.
Assuming 
the absolute value of the gradient of the mapping is
everywhere approximately 3, except in the central region of the Feature,
which leads to the
sequence 
being uniformly distributed over the range 
.
Hence, the probability of trapping after n iterations has an
exponential distribution: for if 
is the probability of exactly n
iterations to trapping, then there are n-1 iterations where trapping does
not occur, and the probability is 
of one of these occurring; then
there is the final iteration where trapping occurs (the state variable
enters the feature), and for this iteration the probability of trapping
is 
.
Thus
By a similar argument, the probability 
for exactly n iterations to
occur before the state variable leaves the fixed point inside the trap
feature
is also exponentially distributed. If 
is the probability of leaving the
trap in one iteration, then
Given that the added noise is Gaussian,
where 
is the complementary error function.