Overview
Includes exercises for deeper learning and teaching
Introduces a range of modern, unsolved, problems
Helps the reader to an in-depth working through the technical details
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Table of contents (14 chapters)
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Front Matter
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Back Matter
Keywords
About this book
The dream of mathematical modeling is of systems evolving in a continuous, deterministic, predictable way. Unfortunately continuity is lost whenever the `rules of the game' change, whether a change of behavioural regime, or a change of physical properties. From biological mitosis to seizures. From rattling machine parts to earthquakes. From individual decisions to economic crashes.
Where discontinuities occur, determinacy is inevitably lost. Typically the physical laws of such change are poorly understood, and too ill-defined for standard mathematics. Discontinuities offer a way to make the bounds of scientific knowledge a part of the model, to analyse a system with detail and rigour, yet still leave room for uncertainty. This is done without recourse to stochastic modeling, instead retaining determinacy as far as possible, and focussing on the geometry of the many outcomes that become possible when it breaks down.
In this book the foundations of `piecewise-smooth dynamics' theory are rejuvenated, given new life through the lens of modern nonlinear dynamics and asymptotics. Numerous examples and exercises lead the reader through from basic to advanced analytical methods, particularly new tools for studying stability and bifurcations. The book is aimed at scientists and engineers from any background with a basic grounding in calculus and linear algebra. It seeks to provide an invaluable resource for modeling discontinuous systems, but also to empower the reader to develop their own novel models and discover as yet unknown phenomena.
Reviews
“Jeffrey’s book seems ideally suited for a masters-level sem-inar course in which students present the book chapter-by-chapter to each other. … I can definitely recommend Jeffrey’s book for anyone looking to learn more about nonsmooth dynamical systems. … this book is one little puzzle piece that might hopefully motivate mathematicians of various interests to refine and extend methods in the vibrant area of applied dynamical systems.” (Christian Kuehn, SIAM Review, Vol. 61 (3), September, 2019)
Authors and Affiliations
Bibliographic Information
Book Title: Hidden Dynamics
Book Subtitle: The Mathematics of Switches, Decisions and Other Discontinuous Behaviour
Authors: Mike R. Jeffrey
DOI: https://doi.org/10.1007/978-3-030-02107-8
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-030-02106-1Published: 20 December 2018
eBook ISBN: 978-3-030-02107-8Published: 11 December 2018
Edition Number: 1
Number of Pages: XVIII, 521
Number of Illustrations: 211 b/w illustrations, 75 illustrations in colour