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)

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http://dx.doi.org/10.1016/j.jtbi.2014.11.027

Abstract

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: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Faculties > Sciences > School of Mathematics Statistics and Actuarial Science > Applied Mathematics
Depositing User: Daniel Bearup
Date Deposited: 30 Nov 2017 11:58 UTC
Last Modified: 29 May 2019 19:47 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/64317 (The current URI for this page, for reference purposes)
Bearup, Daniel: https://orcid.org/0000-0001-8524-7659
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