71 citations · 484 across the 27 of their papers we have counts for
4 papers · 1 filter
Random Numbers from a Delay Equation
Julian Self, Michael C. Mackey
Delay differential equations (DDE) can have "chaotic" solutions that can be used to mimic Brownian motion. Since a Brownian motion is random in its velocity, it is reasonable to th…
A mathematical model of granulopoiesis incorporating the negative feedback dynamics and kinetics of G-CSF/neutrophil binding and internalisation
Morgan Craig, Antony R Humphries, Michael C Mackey
We develop a physiological model of granulopoiesis which includes explicit modelling of the kinetics of the cytokine granulocyte colony-stimulating factor (G-CSF) incorporating bot…
The Limiting Dynamics of a Bistable Molecular Switch With and Without Noise
Michael C. Mackey, Marta Tyran-Kaminska
We consider the dynamics of a population of organisms containing two mutually inhibitory gene regulatory networks, that can result in a bistable switch-like behaviour. We completel…
Response of an oscillatory differential delay equation to a single stimulus
Michael C. Mackey, Marta Tyran-Kaminska, Hans-Otto Walther
Here we analytically examine the response of a limit cycle solution to a simple differential delay equation to a single pulse perturbation of the piecewise linear nonlinearity. We…