© 2018

Hyperbolic and Kinetic Models for Self-organised Biological Aggregations

A Modelling and Pattern Formation Approach


  • Discusses various hyperbolic and kinetic mathematical models for stationary and moving biological/ecological aggregations formed in response to local and nonlocal social interactions

  • Demonstrates how stability and bifurcation theory combined with numerical simulations can be used to investigate and classify the spatio-temporal patterns displayed by these mathematical models

  • Includes real-world examples


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

  1. 1.Division of MathematicsUniversity of DundeeDundeeUK

About the authors

Dr. Eftimie completed her PhD in Applied Mathematics at the University of Alberta, Canada. For her PhD work on the modelling and classification of aggregation patterns in self-organised biological aggregations (which could result from various inter-individual communication mechanisms), she was honoured with the 2008 CAIMS Cecil Graham Doctoral Dissertation Award (Canada). Dr. Eftimie is currently a Reader (Associate Professor) of Applied Mathematics at the University of Dundee, United Kingdom. 

Bibliographic information


“The monograph can primarily be used as a research companion, as it provides a vivid perspective of the state-of-art in its field. … The monograph, which is largely self-contained, can also be used as a basis for a graduate course or a research seminar on self-organized biological aggregation, the dual analytical and numerical perspective allowing for some tailoring to different purposes.” (Paul Georgescu, zbMATH 1415.92002, 2019)