Analysis of the functional dependence of the modified parity-condition parameter on its argument for an important class of Lanchester-type equations for modern warfare†

Abstract

This paper analytically studies the functional dependence of the modified parity. condition parameter on its argument for an important class of Lanchester-type equations for modern warfare with time-dependent attrition-rate coefficients. For such simulated combat between two homogeneous forces, previous research has shown that the prediction of which force (if any) will be annihilated involves the initial force ratio and generally two so-called parity-condition parameters, which are functionals depending on only the attrition-rate coefficients and sometimes coalesce into a, single value. When the appropriate force-level equation is transformed to the normal form for a second-order linear differential equation, the modified parity-condition parameter arises and facilitates certain key numerical determinations. The paper at hand studies the modified parity-condition parameter corresponding to a particular normal-form invariant and. shows it to be a convex function with certain other interesting properties. ...