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Modeling with Nonsmooth Dynamics

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概要 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.続きを見る
目次 Mathematics for a nonsmooth world
1930-2010: Nonsmooth dynamics' linear age
Discontinuities to model missing knowledge
Three experiments
Layers and implementations
Ideal and non-ideal sliding
The three experiments revisited
Further curiosities of hidden dynamics
Closing remarks: open challenges. .
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本文を見る Full text available from Springer Mathematics and Statistics eBooks 2020 English/International

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登録日 2020.06.27
更新日 2020.06.28