Geoscience Reference
In-Depth Information
The formal properties of this model are well known, but it is not simple to
determine the shape of the term CK (that is the demographic potential of the spatial
unit) from the thematic point of view. In addition, in an evolving system, such a
potential is rarely fixed. It depends in particular on the relative place that occupies
the municipality in the spatial system in which it is embedded (for example, its
position relatively to a larger urban center). In order to take into account the effects
of such spatial interactions Allen [ALL 97] develops a system of coupled differential
equations.
Figure 2.2
.
Logistic growth
Dynamic model of a spatial system
Let us suppose that the respective demographic growth of a set of municipalities
making up a system is the point of interest. The underlying hypothesis of such an
approach is that the interactions between the municipalities are the driving force of
change. The point is then to develop a model that takes into account the growth
differentials between the communes. The model, again shaped in the form of global
logistics, may in this case be written in the form of a coupled equations system
whose general term would be, for example:
dP
i
/dt = a P
i
(1 - P
i
/C
i
) , i = 1,….., n
with C
i
= f (E
i
, A
i
/∑A
j
)
where P
i
represents the population in the municipality i,
a
is the rate of growth
(global parameter) and C
i
is the carrying capacity of the municipality
i
. This term is
expressed as a function of a characteristic E
i
of the municipality (for example, its
economic potential) and the attractiveness A
i
of this municipality (for example,
residential potential) relatively to that of other municipalities
j
. This formalization
