Work

Global Bifurcation of Periodic Solutions in Delay Equations with Symmetric Monotone Feedback

Year: 2026

Type: article

Abstract: . We study the periodic solutions of the scalar delay equation [Formula: see text], where [Formula: see text] is strictly monotone in the delayed component and has even-odd symmetry. We completely describe the global bifurcation structure of periodic solutions via a period map originating from planar ordinary differential equations. Moreover, we prove that the first derivative of the period map determines the local stability of the periodic orbits. This article builds on the pioneering work of Kaplan and Yorke, who found some symmetric periodic solutions for [Formula: see text] with even-odd symmetry. We enhance their results by proving that all periodic solutions are symmetric if [Formula: see text] is in addition monotone.

Source: SIAM Journal on Mathematical Analysis

DOI: 10.1137/24m1698110

Author: Alejandro López-Nieto

Institution: National Taiwan University

Language: English

Topic: Nonlinear Differential Equations Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science and Technology Council, Freie Universität Berlin, National Science and Technology Council

OpenAlex ID: W7212014751

FWCI:

Cites: 24

Cited by: 2

Related to: