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

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 reinforcement strategies; constant, and linearly and quadratically varying (with respect to post-battle troop levels) are investigated. It is shown that while a constant reinforcement 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 re-enforcement can lead to stalemate, with quasi-periodic and chaotic behaviour, and the creation of fractal partitioning of the army strength space.