Battle-outcome prediction for an extended system of Lanchester-type differential equations

Battle-outcome-prediction conditions are given for an extended system of Lanchester-type differential equations for two different types of battle-termination conditions: (a) fixed-force-level-breakpoint battles, and (b) fixed-force-ratio-breakpoint battles. Necessary and sufficient conditions for predicting battle outcome are given in the former case for a fight to the finish, while sufficient conditions are given in the latter case. The former results are equivalent to those for the problem of classical analysis of determining (explicitly as a function of the initial conditions) the occurrence of a zero point for the solution to this extended system, although such results as given here have not appeared previously for nonoscillatory (in the strict sense) solutions.