Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Uniqueness of relaxation oscillations: A classical approach

Authors: S. P. Hastings and J. B. McLeod
Journal: Quart. Appl. Math. 73 (2015), 201-217
MSC (2010): Primary 34C26; Secondary 37C27
DOI: https://doi.org/10.1090/S0033-569X-2015-01379-6
Published electronically: March 16, 2015
MathSciNet review: 3357492
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: In a recent paper (Kosiuk and Szmolyan (2011)), the authors discuss a relaxation oscillator which apparently has not been put in standard Lienard form. They use geometric perturbation theory to analyze this model. Their main result is the existence and uniqueness of a periodic solution for small values of two parameters, $ \delta $ and $ \varepsilon ,$ and the behavior of this solution as $ \delta $ and $ \varepsilon $ tend to zero. We show how standard ode methods can be used to give shorter and more direct proofs of these results. Along the way we give a new proof of a more general result.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2010): 34C26, 37C27

Retrieve articles in all journals with MSC (2010): 34C26, 37C27

Additional Information

S. P. Hastings
Affiliation: Department of Mathematics, University of Pittsburgh
Email: sph@pitt.edu

J. B. McLeod
Affiliation: Mathematical Institute, Oxford University

DOI: https://doi.org/10.1090/S0033-569X-2015-01379-6
Received by editor(s): January 12, 2013
Published electronically: March 16, 2015
Additional Notes: The second author is deceased (August 20, 2014).
Article copyright: © Copyright 2015 Brown University

American Mathematical Society