Differential Equation Models for Sharp Threshold Dynamics
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Authors
Schramm, Harrison C.
Dimitrov, Nedialko B.
Subjects
Differential Equations
Markov Population Process
S-I-R Epidemic
Lanchester Model
Markov Population Process
S-I-R Epidemic
Lanchester Model
Advisors
Date of Issue
2012-08
Date
Aug-12
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
We develop an extension to differential equation models of dynamical systems to allow us to analyze probabilistic
threshold dynamics that fundamentally change system behavior. We apply our novel modeling approach to two cases
of interest: a model of cyber infection, where a detection event drastically changes dynamics, and the Lanchester model
of armed conflict, where the loss of a key capability drastically changes dynamics. We derive and demonstrate a stepby-
step, repeatable method for applying our novel modeling approach to an arbitrary system, and we compare the
resulting differential equations to simulations of the system’s random progression. Our work leads to a simple and
easily implemented method for analyzing probabilistic threshold dynamics using differential equations.
Type
Technical Report
Description
Series/Report No
Department
Operations Research
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
NPS-OR-12-003
Sponsors
Funder
Format
Citation
Distribution Statement
Approved for public release; distribution is unlimited.