© 2020

Modeling with Nonsmooth Dynamics


Part of the Frontiers in Applied Dynamical Systems: Reviews and Tutorials book series (FIADS, volume 7)

Table of contents

  1. Front Matter
    Pages i-viii
  2. Mike R. Jeffrey
    Pages 1-14
  3. Mike R. Jeffrey
    Pages 15-20
  4. Mike R. Jeffrey
    Pages 21-24
  5. Mike R. Jeffrey
    Pages 25-33
  6. Mike R. Jeffrey
    Pages 35-43
  7. Mike R. Jeffrey
    Pages 45-57
  8. Mike R. Jeffrey
    Pages 59-73
  9. Mike R. Jeffrey
    Pages 75-79
  10. Mike R. Jeffrey
    Pages 81-83
  11. Back Matter
    Pages 85-104

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.


nonsmooth switch decision discontinuous determinacy Dynamics modeling indeterminacy discontinuity singularity bifurcation switching

Authors and affiliations

  1. 1.Department of Engineering MathematicsUniversity of BristolBristolUK

About the authors

Mike Jeffrey is a researcher and lecturer at the University of Bristol with a background in mathematical physics specializing in dynamics, singularities, and asymptotics.​

Bibliographic information

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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)