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.
This paper reviews how concepts and techniques of system dynamics are being applied in new ways to analyse the operations and formation of artificial and societal systems and then to make decisions about them. The ideas and modelling methods to describe natural and technological systems are mostly reductionist (or ‘bottom-up’) and based on general scientific principles, with ad-hoc elements for any particular system. But very complex and large systems involving science, technology and society, whose complete descriptions and predictions are impossible, can still be designed, controlled and managed using the methods of system dynamics, where they are focused on the outputs of the system in relation to the input data available, and relevant external influences. For many complex systems with uncertain behaviour, their models typically combine concepts and methods of bottom-up system dynamics with statistical modelling of past or analogous data and optimization of outputs. System dynamics that has been generalized by advances in mathematical, scientific and technological research over the past 50 years, together with new approaches to the use of data and ICT, has led to powerful qualitative verbal and schematic concepts as well as improved quantitative methods, both of which have been shown to be of great assistance to decisions, notably about different types of uncertainty and erratic behaviour. This approach complements traditional decision-making methods, by introducing greater clarity about the process, as well as providing new techniques and general concepts for initial analysis, system description – using data in non-traditional ways – and finally analysis and prediction of the outcomes, especially in critical situations where system behaviour cannot be analysed by traditional decision-making methods. The scientific and international acceptance of system methods can make decision-making less implicit, and with fewer cultural assumptions. Topical examples of systems and decision-making are given.
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