Hyperbolic and Kinetic Models for Self-organised Biological Aggregations
A Modelling and Pattern Formation Approach
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Beschreibung
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.
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.
Discusses various hyperbolic and kinetic mathematical models for stationary and moving biological/ecological aggregations formed in response to local and nonlocal social interactions Demonstrates how stability and bifurcation theory combined with numerical simulations can be used to investigate and classify the spatio-temporal patterns displayed by these mathematical models Includes real-world examples
Autor*in
Raluca Eftimie
Themen in »Hyperbolic and Kinetic Models for Self-organised Biological Aggregations«
35Bxx, 35C07, 35Lxx, 35Q20, 35Q92, 35R09, 35R60 92-01, 92-02, 92C15, 92D50 37G40, 58J55, 65Nxx self-organised aggregation animal movement kinetic equations hyperbolic models multiscale models transport equations multiple population models travelling aggregation patterns pattern formation biological and ecological aggregations hyperbolic equations cell movement
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“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)
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