
A Stochastic System and Its Corresponding Deterministic System 359
S3 Generate l independent, uniform random numbers on (0, 1), r
1
, r
2
, . . . , r
l
.
S4 Set t
J
i
= ln(1/r
i
) for i = 1, 2 . . . , l.
S5 Set ∆t
i
= (t
J
i
− t
I
i
)/a
i
for i = 1, 2, . . . , l.
S6 Set ∆t = min
1≤i≤l
{∆t
i
, m
i
(1) − t}.
S7 Set t = t + ∆t.
S8 If ∆t
ι
obtained the minimum in S6, then do the following. If the ι re-
action is an ND, then update the system state according to the reaction
ι. If reaction ι is a C D, then store the time t + τ
ι
in the sec ond to last
position in m
ι
. If reaction ι is an ICD, then update the system state
according to the initiation of the ι reaction and sto re t+τ
ι
in the ...