Overview
- Rather than presenting well-established facts, this book sets out a field in need of the attention of a wide range of theoretical and applied scientists
- A novel range of applied examples are presented, including biological regulation and investment modeling
- An informal style is taken that invites the reader into a conversation on the theory and applications of nonsmooth models
Part of the book series: Frontiers in Applied Dynamical Systems: Reviews and Tutorials (FIADS, volume 7)
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Table of contents (9 chapters)
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Front Matter
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Back Matter
Keywords
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.
Reviews
“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)
Authors and Affiliations
About the author
Bibliographic Information
Book Title: Modeling with Nonsmooth Dynamics
Authors: Mike R. Jeffrey
Series Title: Frontiers in Applied Dynamical Systems: Reviews and Tutorials
DOI: https://doi.org/10.1007/978-3-030-35987-4
Publisher: Springer Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2020
Softcover ISBN: 978-3-030-35986-7Published: 23 February 2020
eBook ISBN: 978-3-030-35987-4Published: 22 February 2020
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
Topics: Dynamical Systems and Ergodic Theory, Mathematical Modeling and Industrial Mathematics