Skip to main content

On time scale invariance of random walks in confined space

Bearup, Daniel, Petrovskii, S. (2014) On time scale invariance of random walks in confined space. Journal of Theoretical Biology, 367 . pp. 230-245. ISSN 0022-5193. (doi:10.1016/j.jtbi.2014.11.027) (KAR id:64317)

PDF Author's Accepted Manuscript
Language: English
Download (921kB) Preview
[thumbnail of Bearup 2015a.pdf]
This file may not be suitable for users of assistive technology.
Request an accessible format
Official URL


Animal movement is often modelled on an individual level using simulated random walks. In such applications it is preferable that the properties of these random walks remain consistent when the choice of time is changed (time scale invariance). While this property is well understood in unbounded space, it has not been studied in detail for random walks in a confined domain. In this work we undertake an investigation of time scale invariance of the drift and diffusion rates of Brownian random walks subject to one of four simple boundary conditions. We find that time scale invariance is lost when the boundary condition is non-conservative, that is when movement (or individuals) is discarded due to boundary encounters. Where possible analytical results are used to describe the limits of the time scaling process, numerical results are then used to characterise the intermediate behaviour.

Item Type: Article
DOI/Identification number: 10.1016/j.jtbi.2014.11.027
Additional information: cited By 3
Uncontrolled keywords: Individual movement; Boundary effect; Self similarity; Brownian motion; Diffusion
Subjects: Q Science > QA Mathematics (inc Computing science)
Q Science > QA Mathematics (inc Computing science) > QA273 Probabilities
Q Science > QA Mathematics (inc Computing science) > QA377 Partial differential equations
Divisions: Divisions > Division of Computing, Engineering and Mathematical Sciences > School of Mathematics, Statistics and Actuarial Science
Depositing User: Daniel Bearup
Date Deposited: 30 Nov 2017 11:58 UTC
Last Modified: 16 Feb 2021 13:50 UTC
Resource URI: (The current URI for this page, for reference purposes)
Bearup, Daniel:
  • Depositors only (login required):


Downloads per month over past year