Dynamical Instability in Combat Models: Computer Arithmetic and Mathematical Models of Attrition and Reinforcement

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[abstract based on the first two paragraphs]

This paper considers two contributing causes of instabilities in combat models and complex simulations. These are (1) computer arithmetic and (2) nonlinear effects, including chaos. The paradigm of dynamics and dynamical systems sets this discussion. A reason for this is that many computations are performed algorithmically. When a computation requires algorithmic iteration, the algorithm functions as a dynamical system which may exhibit computational chaos. Complex models are decision making models that are designed using two or more different interacting modeling paradigms. For this reason combat models are complex models. The design of combat models is based on at least two paradigms: discrete event simulation and algorithmic calculations using computer arithmetic. Vagaries of computer arithmetic cause phase changes and, therefore, timing problems, in computational intensive discrete event simulations of decision making models. Nonlinear effects cause chaos and structural variance in the time evolution of complex models.

Discussions of computer arithmetic are focused on instabilities inherited from real arithmetic. We give a real world example of propagation of timing errors that are a direct effect of computer arithmetic.
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  • Military Operations Research will no longer be hosted by ingentaconnect as of March 1, 2015. Subscriptions and access to issues for subscribers will be available through the MORS website Journal page here: http://www.mors.org/Publications/MOR-Journal For assistance please contact Liz Marriott liz.marriott@mors.org or 703-933-9071.
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