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.