Chemistry Reference
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1.1
1.6
L
E
L
b 1
E
D (2)
D (3)
x 2
x 2
b 1
b 2
D (2)
D (1)
D (1)
b 2
x 1
L
0
0
x 1
1.1
L
1.6
(a)
(b)
Fig. 4.9 Example 4.6; the discrete time model of an N-firm labor-managed oligopoly in the semi-
symmetric case. Linear price function and quadratic labor unit functions. ( a ) The phase space for
L
D
1.( b ) The phase space for L
D
1:5
1.7
1.9
L
L
b 1
D (2)
E
D (2)
b 1
x 2
x 2
E 2
b 2
E 1
E 1
D (1)
D (1)
x 1
x 1
0
L
1.7
0
L
1.9
(a)
(b)
Fig. 4.10 Example 4.6; the discrete time model of an N-firm labor-managed oligopoly in the
semi-symmetric case. Linear price function and quadratic labor unit functions. ( a ) Co-existence of
interior equilibria and their basins of attraction for L
1:8 the second co-existing
equilibrium E 2 has disappeared and E 1 becomes the unique and globally stable attractor
D
1:55,( b )AtL
D
two basins is given by the sta ble set of the sa ddle point E 2 . A further increase of L
above the bifurcation value p d 1 C d 2 D p 3 marks a remarkable qualitative change
in the global dynamic scenario: the boundary equilibrium E and the saddle point
E 2 disappear (they exit the respective regions
.2/ after merging along
the boundary) and the interior equilibrium E 1 remains the unique (and globally sta-
ble) attractor (see Fig . 4.10b obtained for L D 1:8). This explains the sudden jump
.1/
D
and
D
occurring at L D p 3 in the bifurcation diagram of Fig. 4.8.
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