Hyperbolic and Kinetic Models for Self-organised Biological Aggregations: A Modelling and Pattern Formation Approach

✍ Scribed by Raluca Eftimie

Publisher: Springer International Publishing
Year: 2018
Tongue: English
Leaves: 288
Series: Lecture Notes in Mathematics 2232
Edition: 1st ed.
Category: Library

No coin nor oath required. For personal study only.

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xiii
Introduction (Raluca Eftimie)....Pages 1-36
A Short Introduction to One-Dimensional Conservation Laws (Raluca Eftimie)....Pages 37-53
One-Equation Local Hyperbolic Models (Raluca Eftimie)....Pages 55-80
Local Hyperbolic/Kinetic Systems in 1D (Raluca Eftimie)....Pages 81-106
Nonlocal Hyperbolic Models in 1D (Raluca Eftimie)....Pages 107-151
Multi-Dimensional Transport Equations (Raluca Eftimie)....Pages 153-193
Numerical Approaches for Kinetic and Hyperbolic Models (Raluca Eftimie)....Pages 195-226
A Few Notions of Stability and Bifurcation Theory (Raluca Eftimie)....Pages 227-264
Discussion and Further Open Problems (Raluca Eftimie)....Pages 265-273
Back Matter ....Pages 275-280

✦ Subjects

Mathematics; Mathematical and Computational Biology; Theoretical Ecology/Statistics; Partial Differential Equations; Numerical Analysis; Community & Population Ecology; Mathematics of Planet Earth

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