Beyond the Bristol book: Advances and perspectives in non-smooth dynamics and applications

Non-smooth dynamics induced by switches, impacts, sliding, and other abrupt changes are pervasive in physics, biology, and engineering. Yet, systems with non-smooth dynamics have historically received far less attention compared to their smooth counterparts. The classic “Bristol book” [di Bernardo e...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2023-01, Vol.33 (1), p.010402-010402
Main Authors: Belykh, Igor, Kuske, Rachel, Porfiri, Maurizio, Simpson, David J. W.
Format: Article
Language:English
Subjects:
Bifurcations
Biology
Dynamical systems
Dynamics
Multiscale analysis
Sliding
State-of-the-art reviews
Switches
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Summary:Non-smooth dynamics induced by switches, impacts, sliding, and other abrupt changes are pervasive in physics, biology, and engineering. Yet, systems with non-smooth dynamics have historically received far less attention compared to their smooth counterparts. The classic “Bristol book” [di Bernardo et al., Piecewise-smooth Dynamical Systems. Theory and Applications (Springer-Verlag, 2008)] contains a 2008 state-of-the-art review of major results and challenges in the study of non-smooth dynamical systems. In this paper, we provide a detailed review of progress made since 2008. We cover hidden dynamics, generalizations of sliding motion, the effects of noise and randomness, multi-scale approaches, systems with time-dependent switching, and a variety of local and global bifurcations. Also, we survey new areas of application, including neuroscience, biology, ecology, climate sciences, and engineering, to which the theory has been applied.
ISSN:1054-1500
1089-7682
DOI:10.1063/5.0138169