
Hidden Dynamics
The Mathematics of Switches, Decisions & Other Discontinuous Behaviour
Mike R. Jeffrey(Author)
Springer (Publisher)
Published on 11. February 2019
Book
Hardback
XVIII, 521 pages
978-3-030-02106-1 (ISBN)
Description
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.
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 / Votes
"The style of the presentation is enthusiastic, highlighting that the field of study presented is promising. ... In summary, the present book provides an extensive, detailed, and well-written presentation of the field of piecewise-smooth systems whose complete study will allow the interested reader to move from novice to professional." (Jesus M. Gonzalez-Miranda, Mathematical Reviews, October, 2019)More details
Product info
Book
Edition
2018
Language
English
Place of publication
Cham
Switzerland
Publishing group
Springer International Publishing
Target group
Professional and scholarly
Illustrations
68 farbige Tabellen, 211 s/w Abbildungen, 75 farbige Abbildungen
194 schwarz-weiße und 68 farbige Abbildungen, 68 farbige Tabellen, Bibliographie
Dimensions
Height: 241 mm
Width: 160 mm
Thickness: 35 mm
Weight
969 gr
ISBN-13
978-3-030-02106-1 (9783030021061)
DOI
10.1007/978-3-030-02107-8
Schweitzer Classification
Other editions
Additional editions

Mike R. Jeffrey
Hidden Dynamics
The Mathematics of Switches, Decisions and Other Discontinuous Behaviour
E-Book
12/2018
1st Edition
Springer
€128.39
Available for download
Content
Preface.- Chapter Outline.- Chapter 1- Origins of Discontinuity.- Chapter 2- One switch in the Plane: A Primer.- Chapter 3- The Vector Field: Multipliers & Combinations.- Chapter 4- The Flow: Types of Solution.- Chapter 5- The Vector Field Canopy.- Chapter 6- Tangencies: The Shape of the Discontinuity Surface.- Chapter 7- Layer Analysis.- Chapter 8- Linear Switching (Local Theory).- Chapter 9- Nonlinear Switching (Local Theory).- Chapter 10- Breaking Determinacy.- Chapter11- Global Bifurcations & Explosions.- Chapter 12- Asymptotics of Switching: Smoothing & Other Perturbations.- Chapter 13- Four Obsessions of the Two-Fold Singularity.- Chapter 14- Applications from Physics, Biology, and Climate.- Appendix A- Discontinuity as an Asymptotic Phenomenon - Examples.- Appendix B- A Few Words from Filippov & Others, Moscow 1960.- Exercises.- Bibliography.- Glossary.