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.

Autorentext

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.

Inhalt

• 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.