A note on local center manifolds for differential equations with state-dependent delay

TL;DR

This paper constructs local center manifolds for differential equations with state-dependent delay, extending the understanding of invariant manifolds in such functional differential equations.

Contribution

It provides a straightforward method to construct local center manifolds using the Implicit Mapping Theorem for equations with state-dependent delay.

Findings

Existence of local center manifolds established

Method applicable to functional differential equations with delays

Enhances analytical tools for stability analysis

Abstract

In this note we consider local invariant manifolds of functional differential equations representing differential equations with state-dependent delay. Starting with a local center-stable and a local center-unstable manifold of the functional differential equation at a stationary point, we construct, by a straightforward application of the Implicit Mapping Theorem, a local center manifold.