Hyperbolic and Kinetic Models for Self-organised Biological Aggregations

A Modelling and Pattern Formation Approach

  • Raluca Eftimie

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

Also part of the Mathematical Biosciences Subseries book sub series (LNMBIOS, volume 2232)

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Raluca Eftimie
    Pages 1-36
  3. Raluca Eftimie
    Pages 55-80
  4. Raluca Eftimie
    Pages 81-106
  5. Raluca Eftimie
    Pages 107-151
  6. Raluca Eftimie
    Pages 153-193
  7. Raluca Eftimie
    Pages 265-273
  8. Back Matter
    Pages 275-280

About this book


This book focuses on the spatio-temporal patterns generated by two classes of mathematical models (of hyperbolic and kinetic types) that have been increasingly used in the past several years to describe various biological and ecological communities. Here we combine an overview of various modelling approaches for collective behaviours displayed by individuals/cells/bacteria that interact locally and non-locally, with analytical and numerical mathematical techniques that can be used to investigate the spatio-temporal patterns produced by said individuals/cells/bacteria. Richly illustrated, the book offers a valuable guide for researchers new to the field, and is also suitable as a textbook for senior undergraduate or graduate students in mathematics or related disciplines.


35Bxx, 35C07, 35Lxx, 35Q20, 35Q92, 35R09, 35R60 92-01, 92-02, 92C15, 92D50 37G40, 58J55, 65Nxx self-organised aggregation animal movement kinetic equations hyperbolic models multiscale models transport equations multiple population models travelling aggregation patterns pattern formation biological and ecological aggregations hyperbolic equations cell movement inter-individual and inter-cellular communication bifurcation theory numerical simulations stationary aggregation patterns local and non-local interactions

Authors and affiliations

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

Bibliographic information