Differential Equation Models for Sharp Threshold Dynamics
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 step-by-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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 2012
- Accession Number
- ADA567671
Entities
People
- Harrison C. Schramm
- Nedialko B. Dimitrov
Organizations
- Naval Postgraduate School