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The solution of Lanchester’s equations with inter-battle reinforcement strategies

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  • McCartney, Mark

Abstract

A two army conflict made up of repeated battles with inter-battle reinforcements is considered. Each battle is modelled via Lanchester’s ‘aimed fire’ model and three reenforcement strategies; constant, and linearly and quadratically varying (with respect to post-battle troop levels) are investigated. It is shown that while a constant reenforcement strategy will always lead to an outright victory via a simple partitioning of the two dimensional army strength space, linear reinforcement can lead to stalemate, and quadratically varying reinforcement can lead to stalemate, with quasi-periodic and chaotic behaviour, and the creation of fractal partitioning the army space.

Suggested Citation

  • McCartney, Mark, 2022. "The solution of Lanchester’s equations with inter-battle reinforcement strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 586(C).
    • Handle: RePEc:eee:phsmap:v:586:y:2022:i:c:s0378437121007500
    DOI: 10.1016/j.physa.2021.126477
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    References listed on IDEAS

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    1. Ian R. Johnson & Niall J. MacKay, 2011. "Lanchester models and the battle of Britain," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 210-222, April.
    2. Jerome Bracken, 1995. "Lanchester models of the ardennes campaign," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(4), pages 559-577, June.
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