國立虎尾科技大學 |

Hidden Dynamics = The Mathematics of Switches, Decisions and Other Discontinuous Behaviour /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	Hidden Dynamics/ by Mike R. Jeffrey.
Reminder of title:	The Mathematics of Switches, Decisions and Other Discontinuous Behaviour /
Author:	Jeffrey, Mike R.
Description:	XVIII, 521 p. 286 illus., 75 illus. in color.online resource. :
Contained By:	Springer Nature eBook
Subject:	Dynamics. -
Online resource:	https://doi.org/10.1007/978-3-030-02107-8
ISBN:	9783030021078

Hidden Dynamics = The Mathematics of Switches, Decisions and Other Discontinuous Behaviour /
Jeffrey, Mike R.

Hidden DynamicsThe Mathematics of Switches, Decisions and Other Discontinuous Behaviour /[electronic resource] :by Mike R. Jeffrey. - 1st ed. 2018. - XVIII, 521 p. 286 illus., 75 illus. in color.online resource.

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.

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.

ISBN: 9783030021078

Standard No.: 10.1007/978-3-030-02107-8doiSubjects--Topical Terms:

592238
Dynamics.

LC Class. No.: QA313

Dewey Class. No.: 515.39

Hidden Dynamics = The Mathematics of Switches, Decisions and Other Discontinuous Behaviour /
LDR:03830nam a22003975i 4500 001 990246
003 DE-He213
005 20200704083441.0
007 cr nn 008mamaa
008 201225s2018 gw | s |||| 0|eng d
020 $a 9783030021078 $9 978-3-030-02107-8
024 7 $a 10.1007/978-3-030-02107-8 $2 doi
035 $a 978-3-030-02107-8
050 4 $a QA313
072 7 $a PBWR $2 bicssc
072 7 $a MAT034000 $2 bisacsh
072 7 $a PBWR $2 thema
082 0 4 $a 515.39 $2 23
082 0 4 $a 515.48 $2 23
100 1 $a Jeffrey, Mike R. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1211831
245 1 0 $a Hidden Dynamics $h [electronic resource] : $b The Mathematics of Switches, Decisions and Other Discontinuous Behaviour / $c by Mike R. Jeffrey.
250 $a 1st ed. 2018.
264 1 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a XVIII, 521 p. 286 illus., 75 illus. in color. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
505 0 $a 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.
520 $a 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.
650 0 $a Dynamics. $3 592238
650 0 $a Ergodic theory. $3 672355
650 1 4 $a Dynamical Systems and Ergodic Theory. $3 671353
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783030021061
776 0 8 $i Printed edition: $z 9783030021085
856 4 0 $u https://doi.org/10.1007/978-3-030-02107-8
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)