Stability and uniqueness of slowly oscillating periodic solutions to Wright's equation

Jonathan Jaquette, Jean Philippe Lessard, Konstantin Mischaikow

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


In this paper, we prove that Wright's equation y(t)=−αy(t−1){1+y(t)} has a unique slowly oscillating periodic solution (SOPS) for all parameter values α∈[1.9,6.0], up to time translation. Our proof is based on the same strategy employed earlier by Xie [27]; show that every SOPS is asymptotically stable. We first introduce a branch and bound algorithm to control all SOPS using bounding functions at all parameter values α∈[1.9,6.0]. Once the bounding functions are constructed, we then control the Floquet multipliers of all possible SOPS by solving rigorously an eigenvalue problem, again using a formulation introduced by Xie. Using these two main steps, we prove that all SOPS of Wright's equation are asymptotically stable for α∈[1.9,6.0], and the proof follows. This result is a step toward the proof of the Jones’ Conjecture formulated in 1962.

Original languageEnglish (US)
Pages (from-to)7263-7286
Number of pages24
JournalJournal of Differential Equations
Issue number11
StatePublished - Dec 5 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics


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


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