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Nonlocal Hyperbolic Models in 1D

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Hyperbolic and Kinetic Models for Self-organised Biological Aggregations

Part of the book series: Lecture Notes in Mathematics ((LNMBIOS,volume 2232))

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Abstract

More and more experimental studies show that nonlocal interactions play a role in the majority of biological aggregations. In this chapter we describe a few classes of hyperbolic models that include nonlocal interactions among cells/bacteria/animals, which can influence (1) their turning behaviour, (2) their speeding behaviour, or (3) both turning and speeding behaviours. In addition to emphasising the complexity of the numerical patterns that can be exhibited by these nonlocal models, we also present in more detail some analytical approaches, such as bifurcation theory or parabolic limits, that are being used to classify the various patterns exhibited by these nonlocal models. We conclude by discussing the patterns exhibited by a class of nonlocal models that incorporate explicitly stochastic environmental effects that could impact animal movement.

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  1. Division of Mathematics, University of Dundee, Dundee, UK

    Raluca Eftimie

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  1. Raluca Eftimie
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Eftimie, R. (2018). Nonlocal Hyperbolic Models in 1D. In: Hyperbolic and Kinetic Models for Self-organised Biological Aggregations. Lecture Notes in Mathematics(), vol 2232. Springer, Cham. https://doi.org/10.1007/978-3-030-02586-1_5

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