Abstract
In this paper, we prove that Wright's equation y′(t)=−αy(t−1){1+y(t)} has a unique slowly oscillating periodic solution for parameter values α∈([Formula presented],1.9], up to time translation. This result proves Jones' Conjecture formulated in 1962, that there is a unique slowly oscillating periodic orbit for all α>[Formula presented]. Furthermore, there are no isolas of periodic solutions to Wright's equation; all periodic orbits arise from Hopf bifurcations.
Original language | English (US) |
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Pages (from-to) | 3818-3859 |
Number of pages | 42 |
Journal | Journal of Differential Equations |
Volume | 266 |
Issue number | 6 |
DOIs | |
State | Published - Mar 5 2019 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics
Keywords
- Branch and bound
- Computer-assisted proofs
- Delay differential equations
- Jones' conjecture
- Krawczyk method
- Wright's equation