Dimension reduction for stochastic dynamical systems forced onto a manifold by large drift

A constructive approach with examples from theoretical biology

Todd L. Parsons, Tim Rogers

Research output: Contribution to journalArticle

7 Citations (Scopus)
31 Downloads (Pure)

Abstract

Systems composed of large numbers of interacting agents often admit an effective coarse-grained description in terms of a multidimensional stochastic dynamical system, driven by small-amplitude intrinsic noise. In applications to biological, ecological, chemical and social dynamics it is common for these models to posses quantities that are approximately conserved on short timescales, in which case system trajectories are observed to remain close to some lower-dimensional subspace. Here, we derive explicit and general formulae for a reduced-dimension description of such processes that is exact in the limit of small noise and well-separated slow and fast dynamics. The Michaelis-Menten law of enzyme-catalysed reactions, and the link between the Lotka-Volterra and Wright-Fisher processes are explored as a simple worked examples. Extensions of the method are presented for infinite dimensional systems and processes coupled to non-Gaussian noise sources.

Original languageEnglish
Article number415601
JournalJournal of Physics A: Mathematical and Theoretical
Volume50
Issue number41
Early online date17 Aug 2017
DOIs
Publication statusPublished - 8 Sep 2017

Fingerprint

Stochastic Dynamical Systems
Dimension Reduction
biology
dynamical systems
Biology
Dynamical systems
Social Dynamics
Non-Gaussian Noise
Lotka-Volterra
Infinite-dimensional Systems
Enzymes
Trajectories
enzymes
Time Scales
Subspace
trajectories
Trajectory
Model

Keywords

  • dimension reduction
  • dynamical systems
  • Stochastic processes
  • timescale separation

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Modelling and Simulation
  • Mathematical Physics
  • Physics and Astronomy(all)

Cite this

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