Equilibrium solutions, stabilities and dynamics of Lanchester's equations with optimization of initial force commitments.
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Authors
Ang, Bing Ning
Subjects
Lanchester's Equations
Equilibrium Solutions
Stabilities
Domains of Attractions
Initial Force Commitments
Equilibrium Solutions
Stabilities
Domains of Attractions
Initial Force Commitments
Advisors
Moose, Paul H.
Date of Issue
1984-09
Date
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
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.
Type
Thesis
Description
Series/Report No
Department
Organization
Naval Postgraduate School
Identifiers
NPS Report Number
Sponsors
Funder
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.