Abstract
Sections 4.3 and 7.3 introduced us to complex sliding modes as non-trivial attractors in the switching layer. The complexity arose due to non-idealities of the implementation, but it can also occur in ideal piecewise-smooth models due to hidden terms creating non-trivial sliding attractors. We give a brief overview here of a few examples presented in [82].
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
M.R. Jeffrey, Smoothing tautologies, hidden dynamics, and sigmoid asymptotics in piecewise smooth ODEs. Chaos 23, 103125 (2015)
M.R. Jeffrey, Hidden Dynamics: The Mathematics of Switches, Decisions, and Other Discontinuous Behaviour (Springer, Berlin, 2019)
A. Machina, R. Edwards, P. van den Dreissche, Singular dynamics in gene network models. SIADS 12(1), 95–125 (2013)
Y. Ueda, Randomly transitional phenomena in the system governed by Duffing’s equation. J. Stat. Phys. 20, 181–196 (1979)
Y. Ueda, Explosion of strange attractors exhibited by Duffing’s equation, in Nonlinear Dynamics (New York Academy of Science, New York, 1980), pp. 422–434
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this chapter
Cite this chapter
Jeffrey, M.R. (2020). Further Curiosities of Hidden Dynamics. In: Modeling with Nonsmooth Dynamics. Frontiers in Applied Dynamical Systems: Reviews and Tutorials, vol 7. Springer, Cham. https://doi.org/10.1007/978-3-030-35987-4_8
Download citation
DOI: https://doi.org/10.1007/978-3-030-35987-4_8
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-35986-7
Online ISBN: 978-3-030-35987-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)