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

• Main Author: Jeffrey, Mike R. (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Subjects: Dynamics.; Ergodic theory.; Dynamical Systems and Ergodic Theory.

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...

Table of Contents:

• 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.