The mathematical analysis of multi-insurgency warfare in a non-compact domain
The mathematical principles of multi-insurgence warfare are studied by means of phenomenological mathematical models and non-linear analysis theory. The space G of military interactions allows reinforcements by the warring factions and provides the theatre for a three-way battle between an expeditionary army (Army #1) and two indigenous armies (Army #2, Army #3). The model analyzed in this thesis is the Frank Nani model which is a generalized version of the Lanchester model. Incorporated into the non-linear differential equation of the model are death rates due to non-combat related activities, friendly-fire and desertion. In particular, the effects of logistic troop build-up on the long term outcome of the multi-insurgency conflict are explicitly analyzed. Investigative computer simulations are performed to illustrate some of the battle outcomes such as annihilation of armies, battle stalemates and mutual decimation. Explicit mathematical criteria, in terms of battlefield parameters and killing efficiencies, are derived depicting winning scenarios of the expeditionary army #1^
Smith, Isaac George, "The mathematical analysis of multi-insurgency warfare in a non-compact domain" (2015). ETD Collection for Fayetteville State University. AAI10041250.