Equilibrium solutions, stabilities and dynamics of Lanchester's equations with optimization of initial force commitments.

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Author
Ang, Bing Ning
Date
1984-09Advisor
Moose, Paul H.
Second Reader
Wozencraft, John M.
Metadata
Show full item recordAbstract
Generalized Lanchester- type differential equations are
used to study combat processes. This system of non-linear
equations has multiple equilibrium solutions which can be
determined by a numerical technique called the Continuation
Method. Useful properties pertaining to neighborhood
stability are derived by considering the lowest-dimensional
(1*1) problem. A new set of parameters based on the system
asymptotes is defined and used to characterize stability.
System dynamics are investigated using phase trajectories
which are found to depend on the domains of attraction and
stabilities of surrounding equilibria. The effect of varying
initial force levels (X,Y) is studied by calculating an
objective function which is the difference of the losses at
the end of a multistage battle simulation. Based on the
minimax theorem, a set of mixed strategies for (X,Y) can be
found. For highly unstable warfare with large war resources,
instability can be used to influence battle outcome.