Differential Equation Models for Sharp Threshold Dynamics

dc.contributor.authorSchramm, Harrison C.
dc.contributor.authorDimitrov, Nedialko B.
dc.contributor.corporateNaval Postgraduate School (U.S.)
dc.contributor.departmentOperations Research
dc.dateAug-12
dc.date.accessioned2012-09-17T16:46:38Z
dc.date.available2012-09-17T16:46:38Z
dc.date.issued2012-08
dc.description.abstractWe 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.en_US
dc.description.distributionstatementApproved for public release; distribution is unlimited.
dc.identifier.npsreportNPS-OR-12-003
dc.identifier.urihttps://hdl.handle.net/10945/13755
dc.language.isoen_US
dc.publisherMonterey, California. Naval Postgraduate Schoolen_US
dc.subject.authorDifferential Equationsen_US
dc.subject.authorMarkov Population Processen_US
dc.subject.authorS-I-R Epidemicen_US
dc.subject.authorLanchester Modelen_US
dc.titleDifferential Equation Models for Sharp Threshold Dynamicsen_US
dc.typeTechnical Reporten_US
dspace.entity.typePublication
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