A proof of Jones' conjecture

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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 languageEnglish (US)
Pages (from-to)3818-3859
Number of pages42
JournalJournal of Differential Equations
Issue number6
StatePublished - Mar 5 2019
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


  • Branch and bound
  • Computer-assisted proofs
  • Delay differential equations
  • Jones' conjecture
  • Krawczyk method
  • Wright's equation


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