Mathematical modeling and analysis of multi-insurgency combat problem
Warfare involving three mutually antagonistic armies is modeled using a coupled system of non-linear differential equations. In particular the model equations are the Frank Nani generalization of the Lanchester equations so as to incorporate realistic battlefield conditions such as the dynamics of troop surges, friendly fire, and non-combat related deaths. The three armies are presupposed to be using weapons of similar firepower and engaged in conventional warfare. Mathematical techniques involved in this analysis included non-linear systems theory, principles of linearized stability, Hartman-Grobman theory, linear algebraic methods and Real Analysis. In particular, this research analyzes the critical effects of initial troop build-up, troop reinforcement, and the timing of implementation of troop surges. Computer simulations are performed to elucidate some of the outcomes of battle using plausible battlefield scenarios.
Moise, Bernadel, "Mathematical modeling and analysis of multi-insurgency combat problem" (2015). ETD Collection for Fayetteville State University. AAI1581862.