Hyperbolic and Kinetic Models for Self-organised Biological Aggregations
Springer International Publishing (Verlag)
978-3-030-02585-4 (ISBN)
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.
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.
- Introduction. - A Short Introduction to One-Dimensional Conservation Laws. - One-Equation Local Hyperbolic Models. - Local Hyperbolic/Kinetic Systems in 1D. - Nonlocal Hyperbolic Models in 1D. - Multi-Dimensional Transport Equations. - Numerical Approaches for Kinetic and Hyperbolic Models. - A Few Notions of Stability and Bifurcation Theory. - Discussion and Further Open Problems.
"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)
“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)
| Erscheinungsdatum | 09.01.2019 |
|---|---|
| Reihe/Serie | Lecture Notes in Mathematics | Mathematical Biosciences Subseries |
| Zusatzinfo | XIII, 280 p. 73 illus., 59 illus. in color. |
| Verlagsort | Cham |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Gewicht | 456 g |
| Themenwelt | Informatik ► Weitere Themen ► Bioinformatik |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | 35Bxx, 35C07, 35Lxx, 35Q20, 35Q92, 35R09, 35R60 • 35Bxx, 35C07, 35Lxx, 35Q20, 35Q92, 35R09, 35R60 • 37G40, 58J55, 65Nxx • 92-01, 92-02, 92C15, 92D50 • animal movement • Bifurcation Theory • biological and ecological aggregations • cell movement • Hyperbolic equations • Hyperbolic Models • inter-individual and inter-cellular communication • kinetic equations • local and non-local interactions • multiple population models • multiscale models • Numerical simulations • pattern formation • self-organised aggregation • stationary aggregation patterns • transport equations • travelling aggregation patterns |
| ISBN-10 | 3-030-02585-3 / 3030025853 |
| ISBN-13 | 978-3-030-02585-4 / 9783030025854 |
| Zustand | Neuware |
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