BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Jonathan Jaquette (Boston University\, USA)
DTSTART:20210511T140000Z
DTEND:20210511T150000Z
DTSTAMP:20260423T005725Z
UID:CRM-CAMP/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CRM-CAMP/49/
 ">A computer assisted proof of Wright's conjecture: counting and discounti
 ng slowly oscillating periodic solutions to a DDE</a>\nby Jonathan Jaquett
 e (Boston University\, USA) as part of CRM CAMP (Computer-Assisted Mathema
 tical Proofs) in Nonlinear Analysis\n\n\nAbstract\nA classical example of 
 a nonlinear delay differential equation is Wright's equation: $y'(t) = −
 \\alpha y(t − 1)[1 + y(t)]$\, considering $\\alpha > 0$ and $y(t) > -1$.
  This talk discusses two conjectures associated with this equation: Wright
 's conjecture\, which states that the origin is the global attractor for a
 ll $\\alpha \\in ( 0 \, \\pi/2]$\;  and Jones' conjecture\, which states t
 hat there is a unique slowly oscillating periodic solution for $\\alpha > 
 \\pi /2 $. \n\nTo prove Wright's conjecture our approach relies on a caref
 ul investigation of the neighborhood of the Hopf bifurcation occurring at 
 $\\alpha = \\pi/ 2$. Using a rigorous numerical integrator we characterize
  slowly oscillating periodic solutions and calculate their stability\, pro
 ving Jones' conjecture for $\\alpha \\in [1.9\,6.0]$ and thereby all $\\al
 pha \\geq 1.9$. We complete the proof of Jones conjecture using global opt
 imization methods\, extended to treat infinite dimensional problems.\n
LOCATION:https://researchseminars.org/talk/CRM-CAMP/49/
END:VEVENT
END:VCALENDAR