Through Lemma 1, the Nth subnetwork of (12) has [(r + 1).sup.n] locally Mittag-Leffler stable equilibria
[mathematical expression not reproducible].
It turns out that for a very broad class of density functions, there can be multiple stable equilibria
.(4) Such a situation is illustrated in Figure 1.
This is a region in which this stable equilibrium of nonsegregation [P.sub.b] coexists with the two stable equilibria
of segregation (which are stable whatever the values of the entry constraints [K.sub.1] and [K.sub.2]).
hold for all i [member of] [N.sub.2,3] [union] [N.sub.3], then system (2) with activation functions (3) has [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] locally stable equilibria
Case 4: If [[K.sub.1]/[[mu].sub.1]] < [K.sub.2] and [[K.sub.2]/[[mu].sub.2]] < [K.sub.1] then [E.sub.0] is a repeller and is always unstable, [E.sub.1] and [E.sub.2] are stable equilibria
and the interior equilibrium [E.sub.3] is saddle.
Using part (1) of Proposition 1; the fact that the lower branch of the correspondence intersects with the upper right corner shaded region implies that there is a continuum of indeterminate stable equilibria
The conclusion is that all the equilibria in which unemployment depends on efficiency considerations (cases in which the traditional approach would determine full employment) are unstable, whereas all the stable equilibria
correspond to cases in which there would be unemployment even without efficiency wages.
These points at which the ball stops moving represent stable equilibria
. They are stable in that, if the ball is in the point's "neighborhood," (i.e., the sloped area that surrounds the point), then the ball will be attracted to that particular point.
Here, there are two locally stable equilibria
, one symmetric (with half the manufacturers located in each region) and one core periphery.
This increase generates a reduction in F([theta][[[rho].sub.i]]) so that the equilibrium conjecture must decline in all stable equilibria
. This uniform technological worsening is shown in Figure 4 as a downward shift of the graph in Figure 2.
(2.) There could be a single stable equilibrium or more than two stable equilibria
These parameter values are not intended to be close representations of particular natural populations, but have been chosen to generate a range of patterns of dynamics, including stable equilibria
and cyclical behavior with various periodicities.