Normal Vectors on Modified Hopf Manifolds of Delay Differential Equations

TL;DR

This paper derives the normal vector system for modified Hopf boundaries in delay differential equations with state and parameter-dependent delays, providing a proof for a key proposition in the context of robust optimization.

Contribution

It introduces the normal vector system for modified Hopf boundaries in delay differential systems with state and parameter-dependent delays, along with a formal proof of a related proposition.

Findings

Normal vector system for modified Hopf boundaries derived

Proof of Proposition 1 provided

Applicable to delay differential equations with state and parameter-dependent delays

Abstract

This document states the normal vector system for modified Hopf boundaries of delay differential systems with state and parameter dependent delays. Specifically, it states the proof for Proposition 1 in the paper entitled "Robust optimization of delay differential equations with state and parameter dependent delays" by the same authors [1].