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The task of modelling the evolution of cities - the dynamics - is
one of the major challenges of the social sciences. This book
presents mathematical and computer models of urban and regional
dynamics and shows how advances in computer visualisation provide
new insights. Models of non-linear systems in general have three
characteristics: multiple equilibria, 'path dependence' over time
and phase transitions - that is, abrupt change at critical
parameter values. These phenomena all exhibit themselves in
reality, and it is an ongoing task to match model-based analysis
with real phenomena. There are three key features of cities and
regions to be represented in models: activities at a location -
residence, health, education, work and shopping; flows between
locations - spatial interaction; and the structures that carry
these activities - buildings, transport and communications
networks. Spatial interaction and many elements of activities'
location can be modelled by statistical averaging procedures, which
are related to Boltzmann's methods in statistical mechanics. This
is while the evolution of structure can be represented in equations
that connect to the Lotka-Volterra equations in ecology. Within
this broad framework, alternative approaches can be brought to
bear. This book uses entropy-maximising versions of spatial
interaction models. The authors explore the dynamics in more
detail, using advanced visualisation techniques. These ideas have
wide potential uses, and the book illustrates this with
applications in history and archaeology.
The task of modelling the evolution of cities - the dynamics - is
one of the major challenges of the social sciences. This book
presents mathematical and computer models of urban and regional
dynamics and shows how advances in computer visualisation provide
new insights. Models of non-linear systems in general have three
characteristics: multiple equilibria, 'path dependence' over time
and phase transitions - that is, abrupt change at critical
parameter values. These phenomena all exhibit themselves in
reality, and it is an ongoing task to match model-based analysis
with real phenomena. There are three key features of cities and
regions to be represented in models: activities at a location -
residence, health, education, work and shopping; flows between
locations - spatial interaction; and the structures that carry
these activities - buildings, transport and communications
networks. Spatial interaction and many elements of activities'
location can be modelled by statistical averaging procedures, which
are related to Boltzmann's methods in statistical mechanics. This
is while the evolution of structure can be represented in equations
that connect to the Lotka-Volterra equations in ecology. Within
this broad framework, alternative approaches can be brought to
bear. This book uses entropy-maximising versions of spatial
interaction models. The authors explore the dynamics in more
detail, using advanced visualisation techniques. These ideas have
wide potential uses, and the book illustrates this with
applications in history and archaeology.
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