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