HIERARCHAL INDUCTIVE PROCESS MODELING AND ANALYSIS ...

Using the exogenous variables time-series we estimate:
0.009868042 ≤
[
]
(1 − E ice (t)) ∗ a 0 ∗ e (0.06933∗E T H 2 O(t))
≤ 0.6060888 (25)
Using (24), (37) and dropping the subtracted elements we find the upper bound to
be,
We may rewrite as follow,
dP
[
]
dt ≤ (0.6060888)(1)(1 − a 6 ) − (a 9 + a 19 ) P
} {{ }
α u
For the lower bound, since (24) and (23):
dP
≤ α
dt u P where α u = 0.4720906
We may rewrite as follow,
dP
dt ≥ − (a 9 + a 19 ) P − a
} {{ } 13 K
α l
dP
dt
≥ −α l P − K
where α l = 0.032101
Using proposition 1 we get,
∴ (P 0 + K α l
)e −α lt − K α l
≤ P (t) ≤ P 0 e αut (26)
P (t) > 0 ∈ (0, +∞)
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