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From birds to bacteria: generalised velocity jump processes with resting states

Taylor-King, JP; van Loon, E; Rosser, G; Chapman, SJ; (2014) From birds to bacteria: generalised velocity jump processes with resting states. Bull Math Biol , 77 (7) pp. 1213-1236. 10.1007/s11538-015-0083-7. Green open access

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Abstract

There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long-distance movement state and a resting or local movement state. Here, a mathematical description of this process is formulated, adapted from Friedrich et al. (Phys Rev E, 74:041103,2006b). The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of integro-partial differential equations is tumultuous, and therefore, it is necessary to both simplify and derive summary statistics. An expression for the mean squared displacement is derived, which shows good agreement with experimental data from the bacterium Escherichia coli and the gull Larus fuscus. Finally, a large time diffusive approximation is considered via a Cattaneo approximation (Hillen in Discrete Continuous Dyn Syst Ser B, 5:299–318, 2003). This leads to the novel result that the effective diffusion constant is dependent on the mean and variance of the running time distribution but only on the mean of the waiting time distribution.

Type: Article
Title: From birds to bacteria: generalised velocity jump processes with resting states
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s11538-015-0083-7
Publisher version: http://dx.doi.org/10.1007/s11538-015-0083-7
Language: English
Additional information: © The Author(s) 2015. This article is published with open access at Springerlink.com
Keywords: Velocity jump process, Transport equations, Brownian limit, Non-Markov correlated random walk, Mean squared displacement, Effective diffusion
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
URI: https://discovery.ucl.ac.uk/id/eprint/1460314
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