A Criterion for the Existence of Relaxation Oscillations with Applications to Predator-Prey Systems and an Epidemic Model
Abstract
We derive characteristic functions to determine the number and stability of relaxation oscillations for a class of planar systems. Applying our criterion, we give conditions under which the chemostat predator-prey system has a globally orbitally asymptotically stable limit cycle. Also we demonstrate that a prescribed number of relaxation oscillations can be constructed by varying the perturbation for an epidemic model studied by Li et al. [SIAM J. Appl. Math, 2016].
- Publication:
-
arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- 10.48550/arXiv.1811.08307
- arXiv:
- arXiv:1811.08307
- Bibcode:
- 2018arXiv181108307H
- Keywords:
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- Mathematics - Dynamical Systems;
- Mathematics - Classical Analysis and ODEs;
- 34C26;
- 92D25
- E-Print:
- 21 pages, 8 figures