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 and globally change system behavior. We apply
our novel modeling approach to two cases of interest: a model of infectious disease modified for malware
where a detection event drastically changes dynamics by introducing a new class in competition with the
original infection; and the Lanchester model of armed conflict, where the loss of a key capability drastically
changes the effectiveness of one of the sides. 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.
Description
The article of record as published may be located at http://dx.doi.org/10.1016/j.mbs.2013.10.009