105
with the various cell types is positive; for zero or negative sums,
the concentration is taken as zero, as seen in the formulas
S
1
(t + 1) = sgn
(
Σ
S
1
(t) + S
4
(t) + S
3
(t)
)
S
2
(t + 1) = sgn
(
Σ
S
1
(t) + S
4
(t) – S
3
(t) – S
5
(t)
)
S
3
(t + 1) = sgn
(
Σ
S
1
(t)
)
S
4
(t + 1) = sgn
(
Σ
S
1
(t)
)
S
5
(t + 1) = sgn
(
Σ
S
4
(t)
)
where S
i
(t) denotes the concentration of the ith component at
time t and the function sgn(x) defi ned on the natural numbers
N
is 1 if x > 0 and 0 otherwise. This model shows the existence
of only two basins of attractions over 2
5
= 32 possible states:
the empty state where all the concentrations are zero, and a
state where only activated killers disappear while the other four
concentrations reach unity.
Further generalisations of this model consider the same