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BEYOND SLOW-FAST: RELAXATION OSCILLATIONS IN SINGULARLY PERTURBED NONSMOOTH SYSTEMS

Part of: General theory in ordinary differential equations Stability theory Asymptotic theory Smooth dynamical systems: general theory

Published online by Cambridge University Press:  10 June 2021

SAMUEL JELBART Open the ORCID record for SAMUEL JELBART [Opens in a new window]
SAMUEL JELBART*
Affiliation:
School of Mathematics and Statistics, University of Sydney, Camperdown, New South Wales 2006, Australia
*
e-mail: [email protected]
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Abstract

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Keywords

dynamical systemordinary differential equationgeometric singular perturbation theorynonsmooth systemoscillationdesingularisation

MSC classification

Primary: 37C75: Stability theory
Secondary: 34A34: Nonlinear equations and systems, general 34D15: Singular perturbations 34E15: Singular perturbations, general theory 37C10: Vector fields, flows, ordinary differential equations 37C27: Periodic orbits of vector fields and flows
Type
Abstracts of Australasian PhD Theses
Information
Bulletin of the Australian Mathematical Society , Volume 104 , Issue 2 , October 2021 , pp. 342 - 343
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Copyright
© 2021 Australian Mathematical Publishing Association Inc.

Footnotes

Thesis submitted to the University of Sydney in July 2020; degree approved on 15 October 2020; principal supervisor Martin Wechselberger and co-supervisor Kristian Uldall Kristiansen.

References

Jelbart, S., Kristiansen, K. U., Szmolyan, P. and Wechselberger, M., ‘Singularly perturbed oscillators with exponential nonlinearities’, Preprint, 2019, arXiv:1912.11769.Google Scholar
Jelbart, S., Kristiansen, K. U. and Wechselberger, M., ‘Singularly perturbed boundary-focus bifurcations’, Preprint, 2020, arXiv:2006.06087.CrossRefGoogle Scholar
Jelbart, S., Kristiansen, K. U. and Wechselberger, M., ‘Singularly perturbed boundary-equilibrium bifurcations’, Preprint, 2021, arXiv:2103.09613.CrossRefGoogle Scholar
Jelbart, S. and Wechselberger, M., ‘Two-stroke relaxation oscillators’, Nonlinearity 33(5) (2020), Article ID 2364.CrossRefGoogle Scholar