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A dynamic spatial model of conflict escalation

Published online by Cambridge University Press:  05 November 2015

P. BAUDAINS ,
H.M. FRY ,
T.P. DAVIES ,
A.G. WILSON  and
S.R. BISHOP
P. BAUDAINS
Affiliation:
UCL Department of Security and Crime Science, University College London, 35 Tavistock Square, London, WC1H 9EZ, UK UCL Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
H.M. FRY
Affiliation:
UCL Centre for Advanced Spatial Analysis, University College London, Gower Street, London, WC1E 6BT, UK
T.P. DAVIES
Affiliation:
UCL Department of Security and Crime Science, University College London, 35 Tavistock Square, London, WC1H 9EZ, UK UCL Department of Mathematics, University College London, Gower Street, London, WC1E 6BT, UK
A.G. WILSON
Affiliation:
UCL Centre for Advanced Spatial Analysis, University College London, Gower Street, London, WC1E 6BT, UK
S.R. BISHOP
Affiliation:
UCL Department of Security and Crime Science, University College London, 35 Tavistock Square, London, WC1H 9EZ, UK
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Abstract

In both historical and modern conflicts, space plays a critical role in how interactions occur over time. Despite its importance, the spatial distribution of adversaries has often been neglected in mathematical models of conflict. In this paper, we propose an entropy-maximising spatial interaction method for disaggregating the impact of space, employing a general notion of ‘threat’ between two adversaries. This approach addresses a number of limitations that are associated with partial differential equation approaches to spatial disaggregation. We use this method to spatially disaggregate the Richardson model of conflict escalation, and then explore the resulting model with both analytical and numerical treatments. A bifurcation is identified that dramatically influences the resulting spatial distribution of conflict and is shown to persist under a range of model specifications. Implications of this finding for real-world conflicts are discussed.

Keywords

ConflictSpatial ModellingDifferential Equations
Type
Papers
Information
European Journal of Applied Mathematics , Volume 27 , Issue 3: Mathematical Modelling of Crime and Security , June 2016 , pp. 530 - 553
Copyright
Copyright © Cambridge University Press 2015 

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