TY - JOUR
T1 - Beyond the Bristol book
T2 - Advances and perspectives in non-smooth dynamics and applications
AU - Belykh, Igor
AU - Kuske, Rachel
AU - Porfiri, Maurizio
AU - Simpson, David J.W.
N1 - Funding Information:
We are grateful to Mario Di Bernardo, Chris Budd, and Alan Champneys for their constructive feedback and encouragement. We would also like to thank the authors and reviewers for their truly exceptional contributions to this focus issue. This work was supported by the National Science Foundation under Grant Nos. CMMI-1953135 (to I.B. and M.P.), CMMI-2009270 (to I.B. and R.K.), DMS-1909924 (to I.B.), CMMI-1932187 (to M.P.), and Marsden Fund contract MAU1809 managed by Royal Society Te Apārangi (to D.J.W.S.).
Publisher Copyright:
© 2023 Author(s).
PY - 2023/1/1
Y1 - 2023/1/1
N2 - 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.
AB - 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.
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U2 - 10.1063/5.0138169
DO - 10.1063/5.0138169
M3 - Review article
C2 - 36725634
AN - SCOPUS:85146261695
SN - 1054-1500
VL - 33
JO - Chaos
JF - Chaos
IS - 1
M1 - 010402
ER -