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. F...
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| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Cham :
Springer International Publishing,
2018.
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| Ausgabe: | 1st ed. 2018. |
| Schlagworte: | |
| ISBN: | 9783030021078 |
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Inhaltsangabe:
- 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.