Modified and Extended Oligopolies - Nonlinear Oligopolies: Stability and Bifurcations - page 177

2

x

0

10

S

0

β

1

S

Fig. 4.16 The oligopoly model with intertemporal demand interaction and adaptive adjustment in
the discrete time case. The N-firm symmetric model with iso-elastic price function and linear cost
functions. Bifurcation diagrams with respect to ˇ S when the number of firms is N D 3.Other

parameters are A D 1;c D 0:15;L D 2;a D 1. Stable 2-cycles are born at the bifurcation point

2

x

0

S

0

β

1

S

Fig. 4.17 The oligopoly model with intertemporal demand interaction and adaptive adjustment
in the discrete time case. The N-firm symmetric model with iso-elastic price function and linear
cost functions. Bifurcation diagrams with respect to ˇ S when the number of firms is increased to
N D 4. Other parameter values are as in Fig. 4.16. Note that the stable 2-cycles are now born at

ˇ S D 0, and also the sequence of period-doubling followed by period-halving at some intermediate

values of ˇ S