The Bartlett Centre for Advanced Spatial Analysis



Most of our science which is used to inform policy makers about future social and economic events has been built for systems that are local rather than global and are assumed to behave in ways that are relatively tractable and thus responsive to policy initiatives. Any examination of the degree to which such policy-making has been successful or even informative yields a very mixed picture with such interventions being only partly effective at best, and positively disruptive at worst.

Complexity theory recognizes this dilemma. In this research programme, we will develop new forms of science which address the most difficult of human problems: those that involve global change where there is no organised constituency and whose agencies are largely regarded as being ineffective.

We will argue that global systems tend to be treated in isolation from one another and that the unexpected dynamics that characterises their behaviour is due to their coupling and integration that is all too often ignored.

To demonstrate this dynamics and to develop appropriate policy responses, we will study four related global systems: trade, migration, security (which includes crime, terrorism and military disputes) and development aid, which tends to be determined as a consequence of these three individual systems. The idea that this dynamics results from coupling suggests that to get a clear view of their dynamics and a better understanding of global change, we need to develop integrated and coupled models whose dynamics can be described in the conventional and perhaps not so conventional language of complexity theory: chaos, turbulence, bifurcations, catastrophes, and phase transition.

We will develop three related styles of model: spatial interaction models embedded in predator-prey like frameworks which generate bifurcations in system behaviour, reaction diffusion models that link location to flow, and network models in which epidemic-like diffusion processes can be used to explain how events cascade into one another.

We will apply spatial interaction models to trade and migration, reaction diffusion to military disputes and terrorism, and network models to international crime. We will extend these models to incorporate the generation of qualitative new events such as the emergence of new entities e.g. countries, coupling them together in diverse ways.

We will ultimately develop a generic framework for a coupled global dynamics that spans many spatial and temporal scales and pertains to different systems whose behaviours can be simulated both quantitatively and qualitatively.


Alan Wilson
Principal Investigator, CASA
View Alan's profile
Send Alan an email

Michael Batty
Co-Investigator, CASA
View Mike's profile
Send Mike an email

Peter Baudains
Research Associate, Security and Crime Science

Steven Bishop
Co-Investigator, Maths

Alex Braithwaite
Co-Investigator, Political Science
Send Alex an email

Simone Caschili
Research Associate, CASA

Adam Dennett
Research Associate, CASA
View Adam's profile
Send Adam an email

Rob Downes
Research Associate, CASA/Maths
Send Rob an email

Hannah Fry
Co-Investigator, Maths
View Hannah's profile
Send Hannah an email

Sean Hanna
Co-Investigator, Bartlett School of Graduate Studies
Send Sean an email

Shane Johnson
Co-Investigator, Security and Crime Science
Send Shane an email

Anthony Korte
Research Associate, CASA

Rob Levy
Research Associate, CASA
View Rob's profile
Send Rob an email

Elio Marchione
Research Associate, Security and Crime Science

Pablo Mateos
Co-Investigator, Geography
Send Pablo an email

Francesca Medda
Co-Investigator, Civil, Environmental and Geomatic Engineering
Send Francesca an email

Thomas Oléron Evans
Research Associate, CASA/Maths
View Thomas' profile
Send Thomas an email

Joan Serras
Research Associate, Bartlett School of Graduate Studies
Send Joan an email

Frank Smith
Co-Investigator, Maths
Send Frank an email

Doctoral research students on the ENFOLD-ing project are:
Janina Beiser - Political Science
Kimberley Claydon - Geography
Luca Coconchelli - Civil, Environmental and Geomatic Engineering
Toby Davies - Security and Crime Science
Chris Wray - Department of Computer Science 


Levy, R., Oleron Evans, T. P. and Wilson, A. G. (2014) A global inter-country economic model based on linked input-output models, CASA Working Paper 198

Oléron Evans, T. P. ​& Bishop, S. R.​​, A spatial model with pulsed releases to compare strategies for the sterile insect technique applied to the mosquito Aedes aegypti, Mathematical Biosciences 254, August 2014, 6-27

Sidebottom, A., Ashby, M. and Johnson, S. D (2014) Copper Cable Theft: revisiting the price-theft hypothesis, Journal of Research in Crime and Delinquency, published online 13 March 2014 DOI: 10.1177/0022427814521216

Baudains, P., Johnson, S. D. and Braithwaite, A. M. (2013) Geographic patterns of diffusion in the 2011 London riots, Applied Geography, Volume 45, December 2013, Pages 211-219, ISSN 0143-6228

Oleron-Evans, T. P. and Bishop, S. R. (2013) Static search games played over graphs and general metric spaces. European Journal of Operational Research. Available online 27 June 2013

Parola F., Satta G.and Caschili, S. (2013) Unveiling co-operative networks and ‘hidden families’ in the container port industry. Maritime Policy & Management: The flagship journal of international shipping and port research. DOI:10.1080/03088839.2013.782442

Baudains, P., Braithwaite, A., Johnson, S.D (2013) Target choice during extreme events: a discrete spatial choice model of the 2011 London Riots. Criminology, Article first published online: 5 MAR 2013, DOI: 10.1111/1745-9125.12004

Davies, T. P., Fry, H. M., Wilson, A. G., and Bishop, S. R. (2013) A mathematical model of the London riots and their policing, Nature Scientific Reports 3, Article number: 1303 doi:10.1038/srep01303

Dennett, A. (2013) Inter-Regional Migration in Europe and the Influences of Economic and Labour Market Inequalities, CASA Working Paper 192

Preis, T., Moat, H.S., Stanley, H.E. & Bishop, S.R. (2012) Quantifying the Advantage of Looking Forward, Nature Scientific Reports 2, 350

Hunt, J.C.R., Timoshkina, Y., Baudains, P.J. and Bishop, S.R. (2012). System Dynamics Applied to Operations and Policy Decisions, European Review, 20(3): 324-342

Cristelli, M., Batty, M., and Pietronero, L. (2012) There is More than a Power Law in Zipf, Nature Scientific Reports 2, Article number: 812 doi:10.1038/srep00812

Braithwaite, A. and Johnson, S.D. (2012) Space-time modelling of insurgency and counterinsurgency in Iraq. Journal of Quantitative Criminology, 28(1), 31-48

Baudains, P., Braithwaite, A. and Johnson, S.D. (2012) Spatial Patterns in the 2011 London Riots. A Journal of Policy and Practice. doi: 10.1093/police/pas049

Claydon, K. (2012) A Global Model of Human Migration, CASA Working Paper 186

Dennett, A., and Mateos, P. (2012) Global Migration Modelling: A Review of Key Policy Needs and Research Centres, CASA Working Paper 184

Marchione, E., Johnson, S., and Wilson, A.G. (2012) Modelling Maritime Piracy: A Spatial Approach, CASA Working Paper 182

Dennett, A. (2012) Estimating flows between geographical locations: ‘get me started in’ spatial interaction modelling, CASA Working Paper 181

Fry, H. And Wilson, A.G. (2012) A Dynamic Global Trade Model with Four Sectors: Food, Natural Resources, Manufactured Goods and Labour, CASA Working Paper 178

Dearden, J. and Wilson, A.G., 2011. The Relationship of Dynamic Entropy Maximising and Agent Based Approaches. In Heppenstall, A.J., Crooks, A.T., See, L.M., Batty, M. (eds.) 2011. Agent-based Models of Geographical Systems. Berlin: Springer, Chp. 35, pp. 705-720.

Dennett, A. and Wilson, A.G (2011) A Multi-level Spatial Interaction Modelling Framework for Estimating Interregional Migration in Europe, CASA Working Paper 175

Caschili, S., Medda, F.R., Parola, F. and Ferrari, C. (2011) Cooperation in Container Shipping: A Small World Network of Agreements, CASA Working Paper 173

Caschili, S. and Medda, F.R. (2011) Shipping as a Complex Adaptive System: A New Approach in Understanding International Trade, CASA Working Paper 172

Baudains, P., Fry, H., Davies, T. and Wilson, A.G. (2011) Introducing Space to Mathematical Models of Conflict, CASA Working Paper 171

Wilson, A.G., 2010. Urban and regional dynamics from the global to the local: hierarchies, ‘DNA’ and ‘genetic planning’. Environment and Planning B, 37, pp. 23-30

Batty, M. 2010, Visualising Space-Time Dynamics in Scaling Systems, Complexity, 16, 2, 51-63. 


The academic objectives which include the impacts of this programme are as follows:

  • To explain flow patterns of trade, migration, security (including terrorism, crime and military disputes) and development aid with respect to rapid and unexpected change which we will articulate using conventional theory associated with catastrophe, bifurcation and related methods of nonlinear analysis.
  • To demonstrate that patterns of global change can only be explained when the systems above are linked together, thus developing the idea that rapid and unexpected changes at the global level can only be explained in terms of coupling systems together.
  • To illustrate how different modelling styles from the quantitative to the qualitative can be integrated both in individual systems as well as between systems.
  • To extend such analysis to consider multi-scale, multi-temporal dynamics associated with different characterisations of trade, migration, security and development aid at the regional, country and city scales and over very different time horizons.
  • To develop databases for each of these individual global systems and to calibrate and validate appropriate models of the functioning of such systems before integrating these various data in the quest to explain how coupling these systems provides deeper explanations of global dynamics.

The methodological objectives of this programme are as follows:

  • To develop a new mathematics for coupled global dynamics, building on three accepted approaches: spatial interaction models embedded in nonlinear logistic frameworks, reaction-diffusion models which link location and flow, and network models that enable diffusion.
  • To link spatial interaction to morphogenesis in the trade and migration systems linking Boltzmann-Lotka-Volterra to Turing models in the style associated with Krugman and Venables, to develop reaction-diffusion models to explain changing patterns of terrorism and military disputes, and to develop network models in which such diffusion is captured as epidemic processes, applied to patterns of crime.
  • To extend these models to deal with the emergence of new events or categories, such as countries and cities building on Cederman-Axelrod styles of model, enabling the unexpected dynamics of the global system to be appropriately represented.
  • To develop new approaches to calibrating, validating and disseminating such models through visual environments that depend on Web 2.0 technologies.
modelling spatial analysis social complexity