A proof of Jones' conjecture

2018/01/30 by Jaquette, Jonathan · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1801.09806

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∈ (\tfracπ2, 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> \tfracπ2. Furthermore, there are no isolas of periodic solutions to Wright's equation; all periodic orbits arise from Hopf bifurcations.

Cited by

• A Practical Guide to Rigorously Locate Periodic Orbits in Discrete Dynamics

Related

• Stability and Uniqueness of Slowly Oscillating Periodic Solutions to\n Wright's Equation
• Recent advances about the uniqueness of the slowly oscillating periodic solutions of Wright's equation
• A proof of Wright's conjecture
• Multiple slowly oscillating periodic solutions for x'(t) = f(x(t-1))\n with negative feedback
• On periodic solutions of a Hamilton-Jacobi equation with periodic forcing