The RPF control strategy[3] was used to stabilize both
period-1 and period-2 orbits within chaotic attractors measured
by a time series of the anodic current. A Poincaré section was taken
at the time when the anodic current goes through a minimum. A one-dimensional
return map was constructed from the sequence of current minima where
is the current minimum at the beginning of the nth
Poincaré cycle. The
value of the anodic potential during the nth cycle is
. According to the RPF algorithm,
control is established by adding an increment to the anodic potential
during the nth cycle given by[2,3]
where 
is the unstable fixed point of the target orbit
for the return map obtained for a time series taken
at 
. The value of 
and the constants K and R,
are determined from a precontrol
experimental procedure carried out using an interactive computer
program for data acquisition and display.
The precontrol procedure is described in detail in
references[2,3]. Firstly, the
fixed point 
and
the slope, 
, of the one-dimensional return map was determined by
a least square fitting of the
displayed return map (
versus 
) for a sequence of
current minima collected in the neighborhood of the desired fixed point
with the anodic potential
held constant at 
. Secondly, a sequence of current minima were
collected and displayed as a return map while the anodic potential
is changed back and forth between two values; 
for n
odd and 
for n even. The value of 
was chosen to be about the size of the maximum 
used later during control. If the system is sufficiently dissipative,
as our electrochemical system was, the resulting return map
consists of two curves called the up and back maps formed from
alternate (
, 
) pairs with n odd and even respectively.
The shift in the fixed point per unit 
is measured by least squares
fitting for
the up and back maps
giving 
and 
respectively. The values of K and R were then
calculated using the RPF relations[3]
Typically these control constants, K and R, could be determined within 10--20 minutes (corresponding to approximately 200 cycles of the experimental return map) from the start of data acquisition.
With these control constants available, the control algorithm was
initiated. The anodic potential was changed according to the RPF
algorithm of Eq. 1 whenever a minimum of the anodic
current, 
, came within about 0.2 mA of the measured
fixed point 
.
