Combat modelling with partial differential equations

Keane, Therese

doi:10.1016/j.apm.2010.11.057

Cited by 21 publications

(15 citation statements)

References 27 publications

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“…Cellular automata can be difficult to use for understanding the underlying dynamics of combat as stochasticity can hinder the extraction of conclusions from a model. All scenarios presented here highlight the dangers associated with attributing intelligent reasoning to behaviour shown, when this can be explained quite simply through the effects of the terms in our equations (1) and (2) and the spatial distribution of forces. This can be seen quite simply in the Classic Fronts scenario.…”

Section: Discussionmentioning

confidence: 92%

“…As developed in [1], we begin with the following integro-differential equations in two dimensions. Each equation is separated into three parts, f diff containing the diffusion terms, f vel containing the velocity terms and f react containing the interaction terms.…”

Section: A Pde Modelmentioning

confidence: 99%

“…In [1] a set of partial differential equations for a more spatially realistic approach to combat modelling was proposed. Through the implementation of biological aggregation models, a series of basic scenarios demonstrating cohesive soldier movement throughout the domain regardless of losses incurred through firing effects were explored.…”

Section: Introductionmentioning

confidence: 99%

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Partial Differential Equations versus Cellular Automata for Modeling Combat

Keane

2011

Journal of Defense Modeling & Simulation

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We reproduce apparently complex cellular automaton behaviour with simple partial differential equations as developed in [1]. Our PDE model easily explains behaviour observed in selected scenarios of the cellular automaton wargame ISAAC without resorting to anthropomorphisation of autonomous 'agents'. The insinuation that agents have a reasoning and planning ability is replaced with a deterministic numerical approximation which encapsulates basic motivational factors and demonstrates a variety of spatial behaviours approximating the mean behaviour of the ISAAC scenarios. All scenarios presented here highlight the dangers associated with attributing intelligent reasoning to behaviour shown, when this can be explained quite simply through the effects of the terms in our equations. A continuum of forces is able to behave in a manner similar to a collection of individual autonomous agents, and shows decentralised self-organisation and adaptation of tactics to suit a variety of combat situations.

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Section: Discussionmentioning

confidence: 92%

Section: A Pde Modelmentioning

confidence: 99%

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Partial Differential Equations versus Cellular Automata for Modeling Combat

Keane

2011

Journal of Defense Modeling & Simulation

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“…Our approach falls under the umbrella of combat modeling and has similarities to Lanchester attrition models, search theory, missile defense, salvo equations, and duels (Washburn & Kress, ). The Lanchester Linear Law is often used to model artillery conflict because the attrition rate depends upon attacker fire‐power and defensive density, which is the dynamic in many indirect fire scenarios (Keane, ; Lucas & Turkes, ). The flaming datum problem from search theory (Hohzaki & Washburn, ) has similarities to our setting because a submarine flees after an attack, leaving the enemy scrambling to counter.…”

Section: Literature Reviewmentioning

confidence: 99%

Analysis of artillery shoot‐and‐scoot tactics

Shim

Atkinson

2018

Naval Research Logistics

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Firing multiple artillery rounds from the same location has two main benefits: a high rate of fire at the enemy and improved accuracy as the shooter's aim adjusts to previous rounds. However, firing repeatedly from the same location carries significant risk that the enemy will detect the artillery's location. Therefore, the shooter may periodically move locations to avoid counter‐battery fire. This maneuver is known as the shoot‐and‐scoot tactic. This article analyzes the shoot‐and‐scoot tactic for a time‐critical mission using Markov models. We compute optimal move policies and develop heuristics for more complex and realistic settings. Spending a reasonable amount of time firing multiple shots from the same location is often preferable to moving immediately after firing an initial salvo. Moving frequently reduces risk to the artillery, but also limits the artillery's ability to inflict damage on the enemy.

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“…Other studies have incorporated other mechanisms, such as advection, in an effort to construct more realistic models (Protopopescu and Santoro, 1989;Short et al, 2010a,b;Pitcher, 2010;Keane, 2011). Such models still rely on a number of restrictive assumptions.…”

Section: Introductionmentioning

confidence: 99%

A dynamic spatial model of conflict escalation

et al. 2015

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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.

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Combat modelling with partial differential equations

Cited by 21 publications

References 27 publications

Partial Differential Equations versus Cellular Automata for Modeling Combat

Partial Differential Equations versus Cellular Automata for Modeling Combat

Analysis of artillery shoot‐and‐scoot tactics

A dynamic spatial model of conflict escalation

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