Geo-mathematical modelling: models from complexity science
Sir Alan Wilson, Centre for Advanced Spatial Analysis, University
College London
Mathematical and computer models for a complexity science tool kit
Geographical systems are characterised by locations, activities at
locations, interactions between them and the infrastructures that carry
these activities and flows. They can be described at a great variety of
scales, from individuals and organisations to countries. Our
understanding, often partial, of these entities, and in many cases this
understanding is represented in theories and associated mathematical
models.
In this book, the main examples are models that represent elements of
the global system covering such topics as trade, migration, security and
development aid together with examples at finer scales. This provides an
effective toolkit that can not only be applied to global systems, but
more widely in the modelling of complex systems. All complex systems
involve nonlinearities involving path dependence and the possibility of
phase changes and this makes the mathematical aspects particularly
interesting. It is through these mechanisms that new structures can be
seen to 'emerge', and hence the current notion of 'emergent behaviour'.
The range of models demonstrated include account-based models and
biproportional fitting, structural dynamics, space-time statistical
analysis, real-time response models, Lotka-Volterra models representing
'war', agent-based models, epidemiology and reaction-diffusion
approaches, game theory, network models and finally, integrated models.
Geo-mathematical modelling:
- Presents mathematical models with spatial dimensions.
- Provides representations of path dependence and phase changes.
- Illustrates complexity science using models of trade, migration,
security and development aid.
- Demonstrates how generic models from the complexity science tool kit
can each be applied in a variety of situations
This book is for practitioners and researchers in applied mathematics,
geography, economics, and interdisciplinary fields such as regional
science and complexity science. It can also be used as the basis of a
modelling course for postgraduate students.
