HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

Next we turn our attention to P (t) for which we take M(t) to have the following
bounds:
0 ≤ M(t) ≤ 1, (36)
and using the exogenous variables time-series we estimate:
0.0138249 ≤
[
]
(1 − E ice (t)) ∗ a 0 ∗ e (0.06933∗E T H 2 O(t))
≤ 0.8491189 (37)
Then,
[
dP [ ]
dt = (1 − E ice (t))a 0 e (0.06933∗E T H 2 O(t))
M(t)(1 − a 5 ) − a 8 − a 16
]P
(
(a 12 P 2 )
)
−
Z
Z 2 + a 12 a 13 P 2 ]
[(0.8491189)(1)(1 − a 5 ) − a 8 − a 16
≤
We may rewrite as follow,
} {{ }
α u
P
Using proposition 1 we get,
dP
≤ α
dt u P where α u = 0.806566
∴ 0 ≤ P (t) ≤ P 0 e αut (38)
lim P (t) = ∞ (39)
t→+∞
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