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Hidden Dynamics

Hidden Dynamics: The Mathematics Of Switches, Decisions And Other Discontinuous Behaviour


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.



  • Condition: --
    HPB condition ratings
    • New: Item is brand new, unused and unmarked, in flawless condition.
    • Fine/Like New (F): No defects, little usage. May show remainder marks. Older books may show minor flaws.
    • Very Good (VG): Shows some signs of wear and is no longer fresh. Attractive. Used textbooks do not come with supplemental materials.
    • Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
    • Fair (FR): Obviously well-worn, but no text pages missing. May be without endpapers or title page. Markings do not interfere with readability. Used textbooks do not come with supplemental materials.
    • Poor (P): All text is legible but may be soiled and have binding defects. Reading copies and binding copies fall into this category. Used textbooks do not come with supplemental materials.
    Conditions Guide
  • Format: Hardcover
  • Sold by: --
  • Language: English
  • Publisher: Springer Nature
  • ISBN-13: 9783030021061
  • ISBN: 3030021068
  • Publication Year: 2018
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HPB condition ratings
  • New: Item is brand new, unused and unmarked, in flawless condition.
  • Fine/Like New (F): No defects, little usage. May show remainder marks. Older books may show minor flaws.
  • Very Good (VG): Shows some signs of wear and is no longer fresh. Attractive. Used textbooks do not come with supplemental materials.
  • Good (G): Average used book with all pages present. Possible loose bindings, highlighting, cocked spine or torn dust jackets. Used textbooks do not come with supplemental materials.
  • Fair (FR): Obviously well-worn, but no text pages missing. May be without endpapers or title page. Markings do not interfere with readability. Used textbooks do not come with supplemental materials.
  • Poor (P): All text is legible but may be soiled and have binding defects. Reading copies and binding copies fall into this category. Used textbooks do not come with supplemental materials.
Conditions Guide
HPB condition ratings
  • New: Mint condition or still sealed (SS). Absolutely perfect in every way. New.
  • Fine/Like New (EX): No defects, little sign of use, well cared for. Plays perfectly. Close to new. Not necessarily sealed or unused, but close. Could be an unopened promotional or cut item. Sometimes called: mint-minus.
  • Very Good (VG): Will show some signs that it was played and otherwise handled by a previous owner who took good care of it.
  • Good (G): Attractive and well cared for, but no longer fresh. Minor signs of wear, scuffing or scratching, but will play almost perfectly. For vinyl: barely detectable crackles or pops.
  • Fair (FR): This item is in okay condition. For vinyl: good is not so good and the record may have low level crackles or pops when playing. CD: one or more tracks may skip.
  • Poor (P): Obviously well-worn and handled. Most vinyl collectors will not buy good or below, but some tracks on CD or vinyl will play.
Conditions Guide
HPB condition ratings
  • New: This movie is unopened and brand new.
  • Fine/Like New (EX): Near new. No defects, little sign of use. Plays perfectly. Not necessarily sealed or unused, but close. No skipping; no fuzzy or snowy frames in VHS.
  • Very Good (VG): Attractive and well cared for but no longer fresh. Minor signs of wear, but will play almost perfectly. For VHS: barely detectable distortion or very few fuzzy or snowy frames.
  • Good (G): This item is in okay condition and basically works well. There may be some minor distortion on VHS tape; slight scratching or wear on DVD.
  • Fair (FR): Basically plays, but may be obviously well-worn with some scratching or tape distortion.
  • Poor (P): Disc or tape is intact, but may be scratched or stretched. There may be skips or distortion or product defects.
Conditions Guide
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