Chemistry Reference
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0.15
x
2
T
2
(
F
)
F
x
T
(
F
)
a
2
= 0.2466
x
1
0.3
0.6
(a)
0.15
x
2
T
2
(
F
)
T
6
(
F
)
T
8
(
F
)
T
4
(
F
)
F
T
3
(
F
)
T
7
(
F
)
T
5
(
F
)
T
(
F
)
x
a
2
= 0.26
0.07
0.3
x
1
0.6
(b)
Fig. 3.8
Example 3.4; discrete time oligopoly with isoelastic demand and linear cost functions.
Global dynamics in the semi-symmetric case. (
a
)Ata
2
' 0:2466 a border collision bifurcation
occurs when one of the two periodic points intersects the “folding line” F and a 4-piece chaotic
attractor is born. (
b
)Asa
2
increases to a
2
D 0:26 the chaotic attractor intersects a “folding line”
the two periodic points are close to the saddle point
x, hence they belong to region
.1/
. As the parameter a
2
is further increased, the two periodic points move away
from the fixed point, and one of them intersects the boundary of region
D
.1/
, denoted
as “folding line” F in Fig. 3.8. This first border crossing may produce many kinds
of effects. However, in this case there are no evident effects: if one of the peri-
odic points moves into region
D
.1/
), the
2-cycle remains attracting. This is an example of a border collision without any
.2/
D
(while the other remains in region
D
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