Book description
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.
Table of contents
- Cover
- Title Page
- Notes on Contributors
- Acknowledgements
- About the Companion Website
- Part One: Approaches
-
Part Two: Estimating Missing Data: Bi-proportional Fitting and Principal Components Analysis
- Chapter 2: The Effects of Economic and Labour Market Inequalities on Interregional Migration in Europe
- Chapter 3: Test of Bi-Proportional Fitting Procedure Applied to International Trade
- Chapter 4: Estimating Services Flows
- Chapter 5: A Method for Estimating Unknown National Input–Output Tables Using Limited Data
-
Part Three: Dynamics in Account-based Models
-
Chapter 6: A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour
- 6.1 Introduction
- 6.2 Definition of Variables for System Description
- 6.3 The Pricing and Trade Flows Algorithm
- 6.4 Initial Setup
- 6.5 The Algorithm to Determine Farming Trade Flows
- 6.6 The Algorithm to Determine The Natural Resources Trade Flows
- 6.7 The Algorithm to Determine Manufacturing Trade Flows
- 6.8 The Dynamics
- 6.9 Experimental Results
- References
-
Chapter 7: Global Dynamical Input–Output Modelling
- 7.1 Towards a Fully Dynamic Inter-country Input–Output Model
- 7.2 National Accounts
- 7.3 The Dynamical International Model
- 7.4 Investment: Modelling Production Capacity: The Capacity Planning Model
- 7.5 Modelling Production Capacity: The Investment Growth Approach
- 7.6 Conclusions
- References
- Appendix
- A.1 Proof of Linearity of the Static Model and the Equivalence of Two Modelling Approaches
-
Chapter 6: A Dynamic Global Trade Model With Four Sectors: Food, Natural Resources, Manufactured Goods and Labour
- Part Four: Space-Time Statistical Analysis
- Part Five: Real-Time Response Models
- Part Six: The Mathematics of War
- Part Seven: Agent-Based Models
- Part Eight: Diffusion Models
-
Part Nine: Game Theory
- Chapter 15: From Colonel Blotto to Field Marshall Blotto
-
Chapter 16: Modelling Strategic Interactions in a Global Context
- 16.1 Introduction
- 16.2 The Theoretical Model
- 16.3 Strategic Estimation
- 16.4 International Sources of Uncertainty in the Context of Repression and Rebellion
- 16.5 International Sources of Uncertainty Related to Outcomes
- 16.6 Empirical Analysis
- 16.7 Results
- 16.8 Additional Considerations Related to International Uncertainty
- 16.9 Conclusion
- References
- Chapter 17: A General Framework for Static, Spatially Explicit Games of Search and Concealment
- Part Ten: Networks
- Part Eleven: Integration
- End User License Agreement
Product information
- Title: Approaches to Geo-mathematical Modelling
- Author(s):
- Release date: September 2016
- Publisher(s): Wiley
- ISBN: 9781118922279
You might also like
book
Geographical Modeling
The modeling of cities and territories has progressed greatly in the last 20 years. This is …
article
Twenty Years of Open Innovation
Organizations that practice open innovation draw on external resources to develop new ideas for products and …
book
Computational Economics: Heterogeneous Agent Modeling
Handbook of Computational Economics: Heterogeneous Agent Modeling, Volume Four, focuses on heterogeneous agent models, emphasizing recent …
article
Run Llama-2 Models Locally with llama.cpp
Llama is Meta’s answer to the growing demand for LLMs. Unlike its well-known technological relative, ChatGPT, …