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 to introduce terms to model each army's 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. Subsequently, a generalisation to the classical Lanchester equation to account for "zombie warfare" (coercive recruitment) is also derived, and its key aspects (victory conditions, temporal evolution, and stability) are analysed. Finally, a unified modified model involving both lethality of opponents being diminished by the reciprocal of one's own forces and coercive recruitment is expressed and analysed.