chapter
7 Pages

## IFi}j

definitions attractiveness factor, linearities analytically. clearly different fluctuations. entirely clear distribution initially

Rkj E F. I •i I , J but that given F~~ in (6.28) and the definitions of all thelJ component pieces of that attractiveness factor, then the nonlinearities in the p~ variables are again impossible to handle, analytically. Both k and k' are clearly involved in each equation, but so are the P~IS for each zone because of the

EF~~. term in (6.32). So' once again, an analytical search for • I 1 J , solutions is likely to be unfruitful. This case is, however, simpler than the inter-urban example, and it may te possible to obtain numerically plots of

and then to use a method analogous to that of Section 5.4. In the simulation runs, a different procedure is used to

introduce fluctuations. It is not entirely clear whether the distribution of jobs is given initially and fixed throughout the simulation, or whether there is some growth process from various initial conditions. In either case, it is not clear what the initial conditions are. However, we will assume that a satisfactory procedure is adopted. The random effects are then introduced as follows:

(6.34)

where D~ is the spatial distribution of jobs at a particular time inierval and D~ is a new distribution for the next time interval in the numerical integration of the equations. A is a parameter and Gj is a random number between 0 and 1 scaled so that

The results of the simulation runs do show different patterns of residential segregation developing for a wide series of different parameter values. However, because the data is essentially bypothetical, the main utility of the present model is theoretical. In the next subsection, we briefly review the possibility of working with more general sets of equations and reserve our final comments on the Brussels' model to a context which can include this other approach and this is done in the final Subsection 6.2.4, below.