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Nonlocal Hyperbolic Models in 1D

  • Raluca Eftimie
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2232)

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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Authors and Affiliations

  • Raluca Eftimie
    • 1
  1. 1.Division of MathematicsUniversity of DundeeDundeeUK

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