The results reported in this section all relate to a chain consisting of N=12
cells, with 
, 
, 
and 
for i > 1.
For these values, 
, which is only coupled to itself, generates a chaotic
time series; 
would exhibit period two behaviour if they
were not self-coupled, oscillating between 
.
For these parameter values, the actual output (
) is approximately a
two-level, aperiodic signal --- see figure 3(a).
Furthermore, for these parameter values at least, the overall effect of the
CMC on its input can be well described by a simple thresholding operation:
see figure 3(b), in which the output is equal to 
if the input is 
and is 
otherwise. The threshold
appears to be 
, an unstable fixed point of the mapping
of 
.
This type of behaviour would be expected if for i>1, 
and 
such that
period-2 behaviour resulted ( e.g. 3.2). In that case, none of the cells except
the first is self-coupled. Hence, in travelling down the chain, an initial value
iterates towards one fixed point or the other, and hence thresholding takes
place. Less easily explained is the occurrence of this behaviour when 
.
Figure 3: (a) A typical sample of 
and 
(respectively input and output) waveforms. (b) A comparison of the actual
output with the input thresholded at 0.730.
Furthermore, the output (
) is an approximately one-dimensional
function of the input (
) as can be seen from figure 4.
Figure 4: The transfer function 
vs. 
.
The relationship for these parameter values is one-dimensional for some
ranges of the input, fractal for others -- see inset.