A criterion for the existence of relaxation oscillations with applications to predator-prey systems and an epidemic model
| Autor: | Gail S. K. Wolkowicz, Ting-Hao Hsu |
|---|---|
| Rok vydání: | 2020 |
| Předmět: |
Applied Mathematics
010102 general mathematics Perturbation (astronomy) Dynamical Systems (math.DS) 01 natural sciences 010101 applied mathematics Mathematics - Classical Analysis and ODEs 34C26 92D25 Stability theory Limit cycle Classical Analysis and ODEs (math.CA) FOS: Mathematics Quantitative Biology::Populations and Evolution Discrete Mathematics and Combinatorics Applied mathematics Mathematics - Dynamical Systems 0101 mathematics Epidemic model Mathematics |
| Zdroj: | Discrete & Continuous Dynamical Systems - B. 25:1257-1277 |
| ISSN: | 1553-524X |
| DOI: | 10.3934/dcdsb.2019219 |
| Popis: | 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]. Comment: 21 pages, 8 figures |
| Databáze: | OpenAIRE |
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