Abstract
In this paper, we introduce a method to prove existence of several rapidly and slowly oscillating periodic solutions of a delayed Van der Pol oscillator. The proof is a combination of pen and paper analytic estimates, the contraction mapping theorem and a computer program using interval arithmetic. Using this approach we extend some existence results obtained by Nussbaum (Ann Mat Pura Appl 4(101):263–306, 1974).
| Original language | English |
|---|---|
| Pages (from-to) | 1233-1257 |
| Number of pages | 25 |
| Journal | Journal of Dynamics and Differential Equations |
| Volume | 29 |
| Issue number | 4 |
| Early online date | 01 Aug 2017 |
| DOIs | |
| Publication status | Published - 01 Dec 2017 |
| Externally published | Yes |
Keywords
- Contraction mapping theorem
- Delay differential equations
- Rapid and slow periodic solutions
- Rigorous numerics
- Van der Pol equation
ASJC Scopus subject areas
- Analysis
