Modeling persistence of motion in a crowded environment: The diffusive limit of excluding velocity-jump processes

Physical Review. E
Enrico Gavagnin, Christian A Yates

Abstract

Persistence of motion is the tendency of an object to maintain motion in a direction for short time scales without necessarily being biased in any direction in the long term. One of the most appropriate mathematical tools to study this behavior is an agent-based velocity-jump process. In the absence of agent-agent interaction, the mean-field continuum limit of the agent-based model (ABM) gives rise to the well known hyperbolic telegraph equation. When agent-agent interaction is included in the ABM, a strictly advective system of partial differential equations (PDEs) can be derived at the population level. However, no diffusive limit of the ABM has been obtained from such a model. Connecting the microscopic behavior of the ABM to a diffusive macroscopic description is desirable, since it allows the exploration of a wider range of scenarios and establishes a direct connection with commonly used statistical tools of movement analysis. In order to connect the ABM at the population level to a diffusive PDE at the population level, we consider a generalization of the agent-based velocity-jump process on a two-dimensional lattice with three forms of agent interaction. This generalization allows us to take a diffusive limit and obtain ...Continue Reading

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Citations

Nov 28, 2019·Physical Review. E·Stephen ZhangBarry D Hughes
Jul 28, 2020·Philosophical Transactions of the Royal Society of London. Series B, Biological Sciences·Josué Manik Nava-SedeñoFernando Peruani
Jun 16, 2021·PLoS Computational Biology·Andreas DeutschHaralampos Hatzikirou

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