Dichotomy results for delay differential equations with negative Schwarzian

TL;DR

This paper explores the use of the Schwarzian derivative to derive new results for delay differential equations, providing dichotomy results that help estimate the global attractor and discussing related conjectures and open problems.

Contribution

It introduces new dichotomy results for delay differential equations using the Schwarzian derivative, enabling easier computation of global attractor bounds.

Findings

Derived new bounds for the global attractor.

Established dichotomy results for specific delay differential equations.

Discussed conjectures and formulated open problems.

Abstract

We gain further insight into the use of the Schwarzian derivative to obtain new results for a family of functional differential equations including the famous Wright's equation and the Mackey-Glass type delay differential equations. We present some dichotomy results, which allow us to get easily computable bounds of the global attractor. We also discuss related conjectures, and formulate new open problems.