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 - 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 -