Conjecture on stability of the stalemate equilibrium in Lanchester theory

Let the stalemate equilibrium be the equilibrium defined by Eqs.

$$--$$

for the system of differential equations studied in the paper. Stability conjecture. The stalemate equilibrium is stable if and only if

$$\frac{r_C-A_C}{1+r_C}>S.$$

The theorem preceding this conjecture establishes a necessary stability condition for the Blue victory equilibrium, while the stability characteristics of the stalemate equilibrium had not been proved analytically. Extensive numerical experimentation was reported as evidence for this conjecture.