6
R. Camagni et al.
same advantages and disadvantages to firms and dwellers. This condition remains
valid only when cities share the same size (Camagni 1992, Sect. 6.6).
However, CPT is not free from shortcomings. One such limitation is related to
their inherently static approach: proof being that in these models relative city rankings
remain stable over time. While this result is acceptable over the short/medium run,
it clearly cannot explain long-run urban growth processes. While some have tried to
overcome this limitation at least in terms of comparative statics (Parr 1981), there is
still a chance to explain the diverging development patterns of cities over the long
run.
In this sense, following the newly developed self-organization approach to the
dynamics of complex systems (Prigogine and Stengers 1984) and in particular its
application to the evolution of urban systems (Allen and Sanglier 1981; Dendrinos
and Mullally 1981; Bertuglia et al. 1987), the SOUDY model (Camagni et al. 1986)
introduced a dynamic and evolutionary approach, in theoretical, mathematical and
simulation terms. The dynamics of each city in the model, interacting within urban
systems, happens through two distinct processes:
(i) a process of constrained dynamics, causing demographic growth (within efficient size intervals) towards an attractor (net urban benefits) and linked to the
hierarchical level of each function;
(ii) a process of structural dynamics, engendered by an innovation leap achieved by
each city. This happens through the acquisition of new functions, relating to a
higher hierarchical level, allowing higher profits, balancing the superior costs of
larger dimensions. In the SOUDY model, the probability of transition depends
on an endogenous dynamic instability condition, where each city overcomes the
size threshold for the appearance of the superior function. This can potentially
lead to the acquisition of the new function (or to the loss of previous functions)
and consequently to relevant bifurcations in the development path.
Following up to the conceptual novelties of the SOUDY model, the development
path of cities determined by normal, multiplier-type dynamics and by structural
dynamics led by internal innovation was empirically investigated identifying three
hierarchical ranks (small, medium and large cities) in the European urban system
(Camagni et al. 2015a, b). Interpreting urban growth as net returns to urban scale, the
assumption of an inverted U-shaped relationship between city size and agglomeration
economies inside each rank was found to be statistically significantly verified, along
with the evidence of the possibility, for dynamic cities, to escape decreasing returns
through innovation.
Moreover, Camagni et al. (2015a, b) find that:
(i) the intensity of the following factors determines increasing returns irrespective
of city size: the quality of the activities hosted, the quality of production factors,
the density of external linkages and cooperation networks, the quality of urban
infrastructure—internal and external mobility, education, public services;
(ii) large, as well as medium and small cities, may experience a halt in their growth
path, even a decline, when they grow without a simultaneous increase in the
R. Camagni et al.
same advantages and disadvantages to firms and dwellers. This condition remains
valid only when cities share the same size (Camagni 1992, Sect. 6.6).
However, CPT is not free from shortcomings. One such limitation is related to
their inherently static approach: proof being that in these models relative city rankings
remain stable over time. While this result is acceptable over the short/medium run,
it clearly cannot explain long-run urban growth processes. While some have tried to
overcome this limitation at least in terms of comparative statics (Parr 1981), there is
still a chance to explain the diverging development patterns of cities over the long
run.
In this sense, following the newly developed self-organization approach to the
dynamics of complex systems (Prigogine and Stengers 1984) and in particular its
application to the evolution of urban systems (Allen and Sanglier 1981; Dendrinos
and Mullally 1981; Bertuglia et al. 1987), the SOUDY model (Camagni et al. 1986)
introduced a dynamic and evolutionary approach, in theoretical, mathematical and
simulation terms. The dynamics of each city in the model, interacting within urban
systems, happens through two distinct processes:
(i) a process of constrained dynamics, causing demographic growth (within efficient size intervals) towards an attractor (net urban benefits) and linked to the
hierarchical level of each function;
(ii) a process of structural dynamics, engendered by an innovation leap achieved by
each city. This happens through the acquisition of new functions, relating to a
higher hierarchical level, allowing higher profits, balancing the superior costs of
larger dimensions. In the SOUDY model, the probability of transition depends
on an endogenous dynamic instability condition, where each city overcomes the
size threshold for the appearance of the superior function. This can potentially
lead to the acquisition of the new function (or to the loss of previous functions)
and consequently to relevant bifurcations in the development path.
Following up to the conceptual novelties of the SOUDY model, the development
path of cities determined by normal, multiplier-type dynamics and by structural
dynamics led by internal innovation was empirically investigated identifying three
hierarchical ranks (small, medium and large cities) in the European urban system
(Camagni et al. 2015a, b). Interpreting urban growth as net returns to urban scale, the
assumption of an inverted U-shaped relationship between city size and agglomeration
economies inside each rank was found to be statistically significantly verified, along
with the evidence of the possibility, for dynamic cities, to escape decreasing returns
through innovation.
Moreover, Camagni et al. (2015a, b) find that:
(i) the intensity of the following factors determines increasing returns irrespective
of city size: the quality of the activities hosted, the quality of production factors,
the density of external linkages and cooperation networks, the quality of urban
infrastructure—internal and external mobility, education, public services;
(ii) large, as well as medium and small cities, may experience a halt in their growth
path, even a decline, when they grow without a simultaneous increase in the