Hyperbolic and Kinetic Models for Self-organised Biological Aggregations

A Modelling and Pattern Formation Approach
1. Auflage 2018
ISBN: 978-3-030-02585-4
Verlag: Springer International Publishing

Buch, Englisch, Band 2232, 280 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 452 g

Reihe: Lecture Notes in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Eftimie, Raluca

Fachgebiete

• Naturwissenschaften Biowissenschaften Biowissenschaften Ökologie
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Biomathematik
• Naturwissenschaften Biowissenschaften Angewandte Biologie Bioinformatik
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Mathematische Modellierung

Inhaltsverzeichnis

- 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.

Über Autor(innen)

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.