On the Dynamics, Tactics, and Strategic Implications of Lanchester Models of Combat with Defensive Terms and Exact Time-Domain Solutions

We propose an extension to the classical Lanchester equations which introduces, for each army, a term modelling its ability to defend itself, proportional to its own strength as a denominator under it's opponent's offensive strength. This modification is shown to resolve into a cubic state law. Exact solutions in the time domain are calculated in terms of the Gaussian hypergeometric function. Subsequently, a generalisation of the classical Lanchester equations accounting for coercive recruitment (“zombie warfare”) is derived, and its victory conditions, temporal evolution, and stability are analysed. Finally, a unified model involving both the defensive mechanism and coercive recruitment is formulated and analysed, and an implicit general solution is presented.