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E.m. Thomson - One of the best experts on this subject based on the ideXlab platform.

Robin Lee - One of the best experts on this subject based on the ideXlab platform.

Robin L. Lee - One of the best experts on this subject based on the ideXlab platform.

Brendon A. Bradley - One of the best experts on this subject based on the ideXlab platform.

S. Jon Chapman - One of the best experts on this subject based on the ideXlab platform.

  • From Birds to Bacteria: Generalised Velocity Jump Processes with Resting States
    Bulletin of Mathematical Biology, 2015
    Co-Authors: Jake P. Taylor-king, E. Emiel Loon, Gabriel Rosser, S. Jon Chapman
    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.

  • From birds to bacteria: Generalised Velocity jump processes with resting states
    arXiv: Quantitative Methods, 2014
    Co-Authors: Jake P. Taylor-king, Gabriel Rosser, E. Emiel Van Loon, S. Jon Chapman
    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. (2006). The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of partial integro-differential equations are 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, 2004). 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.