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arXiv · 1811.08307

A Criterion for the Existence of Relaxation Oscillations with Applications to Predator-Prey Systems and an Epidemic Model

Ting-Hao Hsu·Gail S. K. Wolkowicz
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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].

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Ting-Hao Hsu, Gail S. K. Wolkowicz. 2018-11-19. A Criterion for the Existence of Relaxation Oscillations with Applications to Predator-Prey Systems and an Epidemic Model. https://doi.org/10.3934/dcdsb.2019219

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