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Discrete dynamic systems
87
and so on. Hence, each number in the sequence ultimately depends on two initial
values,
y
t
+
1
and
y
t
.
This requirement generalises. For an
m
order dynamic system
m
initial values are generally required for its solution.
Let
y
t
+
1
=
f
(
y
t
)
y
0
at
t
=
0
This represents a
recursive equation
and we can generate a sequence starting
from the value
y
0
. The sequence would be
y
0
,
f
(
y
0
)
,
f
(
f
(
y
0
))
,
f
(
f
(
f
(
y
0
)))
,...
Letting
f
n
(
y
0
) denote the
n
th iterate of
y
0
under
f
, then the sequence can be ex
pressed
y
0
,
f
(
y
0
)
,
f
2
(
y
0
)
,
f
3
(
y
0
)
,...
The set of all (positive) iterates
{
f
n
(
y
0
)
,
n
≥
0
}
is called the (positive)
orbit
of
y
0
.
3.3 The cobweb model: an introduction
Tohighlightthefeaturessofaroutlined,andotherstofollow,considerthefollowing
typical cobweb model in which demand at time
t
,
q
d
t
, depends on the price now
ruling on the market,
p
t
, while the supply at time
t
,
q
s
t
, depends on planting, which
in turn was governed by what the price the farmer received in the last period,
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This note was uploaded on 12/14/2011 for the course ECO 3023 taught by Professor Dr.gwartney during the Fall '11 term at FSU.
 Fall '11
 Dr.Gwartney
 Economics

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