The University of Southampton
Mathematical Sciences

Research project: Equation-free Methods

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Equation-free methods provide a bridge between microscopic descriptions of stochastic systems such as individual-based models, and macroscopic viewpoints of the same system, for example population-level perspectives.

Project Overview

Equation-free methods provide a bridge between microscopic descriptions of stochastic systems such as individual-based models, and macroscopic viewpoints of the same system, for example population-level perspectives. They not only allow for accelerated simulation at the macroscopic level but also enable system-level tasks, such as macroscopic bifurcation analysis. In the equation-free framework, we assume the existence of a closed macroscopic model in terms of a few state variables. However, instead of deriving an approximate macroscopic model analytically, we construct a computational superstructure, wrapped around a microscopic simulation. We have applied equation-free methods to understanding switching in two-component system signalling in bacteria, and have also developed improvements to the efficiency of the equation-free algorithm in the context of opinion dynamics.

© Daniele Avitabile

Publications

D.Avitabile, R.B. Hoyle and G. Samaey [2014] Noise reduction in coarse bifurcation analysis of stochastic agent-based models: an example of consumer lock-in, SIAM J. Appl. Dyn. Syst., 13(4), 1583-1619. PDF Copyright © by SIAM.

R.B. Hoyle, D. Avitabile and A.M. Kierzek [2012] Equation-free analysis of two-component system signalling model reveals the emergence of co-existing phenotypes in the absence of multistationarity. PLoS Comput Biol 8(6): e1002396. doi:10.1371/journal.pcbi.1002396. Postprint with better typesetting.

Staff

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