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

Description

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. 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