Biology Reference
In-Depth Information
Fig. 10. An illustration to show the transitions in conflict and their parameters.
Fig. 11. An example illustrating conflict state.
given as a constant in advance according to the biological facts provided in the published literature.
n
i
n
α
i
represents the total firing number
of transition
t
i
from the beginning. Expression (4) is designed to reserve the token to such a transition
t
i
that has the largest difference between calculated firing probabilities
is used to record the number of tokens that
t
i
has reserved so far;
n
α
i
/
j
=1
n
j
α
j
and given firing
probability
s
i
among all the transitions in conflict.
Delay times of transitions in conflict
We consider the determination of delay times for the transitions in conflict as shown in Fig. 11. The
maximum firing frequency
f
O
j
must satisfy the following inequality according to the above firing rule:
m
s
j
·
α
j
·
f
I
i
·
β
i
f
O
j
·
α
j
(5)
k
=1
s
k
n
·
α
k
i
=1
where
α
j
and
β
i
are the weights of
e
(
p
i
,t
O
j
)
and
e
(
t
I
i
,p
i
)
, respectively;
s
j
is the firing probability of
t
O
j
;
f
I
i
is the firing frequency and
f
O
j
is the maximum firing frequency of
t
I
i
and
O
j
, respectively, as
shown in Fig. 11. The left-hand of expression (5) derives the token amount reserved to the transition
t
O
j
from the total token amount
i
=1
f
I
i
β
i
coming from each input transition connected to the place
p
i
,
while the right-hand represents the possible token amount from
p
i
to its output transition
t
O
j
per time
unit.
·
s
j
·
α
j
k
=1
s
k
·α
k
represents the ratio of the token amount deposited to
t
O
j
to the total token amount from
p
i
to each transition per time unit.
