About this book
This volume looks at the study of dynamical systems with discontinuities. Discontinuities arise when systems are subject to switches, decisions, or other abrupt changes in their underlying properties that require a ‘non-smooth’ definition. A review of current ideas and introduction to key methods is given, with a view to opening discussion of a major open problem in our fundamental understanding of what nonsmooth models are.
What does a nonsmooth model represent: an approximation, a toy model, a sophisticated qualitative capturing of empirical law, or a mere abstraction? Tackling this question means confronting rarely discussed indeterminacies and ambiguities in how we define, simulate, and solve nonsmooth models. The author illustrates these with simple examples based on genetic regulation and investment games, and proposes precise mathematical tools to tackle them.
The volume is aimed at students and researchers who have some experience of dynamical systems, whether as a modelling tool or studying theoretically. Pointing to a range of theoretical and applied literature, the author introduces the key ideas needed to tackle nonsmooth models, but also shows the gaps in understanding that all researchers should be bearing in mind.
Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics, specializing in dynamics, singularities, and asymptotics.
- Book Title Modeling with Nonsmooth Dynamics
- Series Title Frontiers in Applied Dynamical Systems: Reviews and Tutorials
- Series Abbreviated Title Frontiers in Applied Dynamical Systems: Reviews and Tutorials
- DOI https://doi.org/10.1007/978-3-030-35987-4
- Copyright Information Springer Nature Switzerland AG 2020
- Publisher Name Springer, Cham
- eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
- Softcover ISBN 978-3-030-35986-7
- eBook ISBN 978-3-030-35987-4
- Series ISSN 2364-4532
- Series E-ISSN 2364-4931
- Edition Number 1
- Number of Pages VIII, 104
- Number of Illustrations 13 b/w illustrations, 15 illustrations in colour
Dynamical Systems and Ergodic Theory
Mathematical Modeling and Industrial Mathematics
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“This book is best matched to graduate students and researchers with a background in basic dynamical systems. It has an extensive bibliography and would provide a great source for new research problems.” (Bill Satzer, MAA Reviews, September 13, 2020)