Overview
- 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 book series: Lecture Notes in Mathematics (LNM, volume 2232)
Part of the book sub series: Mathematical Biosciences Subseries (LNMBIOS)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
- 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
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.
Reviews
Authors and Affiliations
About the author
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
Book Title: Hyperbolic and Kinetic Models for Self-organised Biological Aggregations
Book Subtitle: A Modelling and Pattern Formation Approach
Authors: Raluca Eftimie
Series Title: Lecture Notes in Mathematics
DOI: https://doi.org/10.1007/978-3-030-02586-1
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Softcover ISBN: 978-3-030-02585-4Published: 08 January 2019
eBook ISBN: 978-3-030-02586-1Published: 07 January 2019
Series ISSN: 0075-8434
Series E-ISSN: 1617-9692
Edition Number: 1
Number of Pages: XIII, 280
Number of Illustrations: 14 b/w illustrations, 59 illustrations in colour
Topics: Mathematical and Computational Biology, Theoretical Ecology/Statistics, Partial Differential Equations, Numerical Analysis, Community & Population Ecology, Mathematics of Planet Earth