On time transformations for differential equations with state-dependent delay

TL;DR

This paper investigates systems of differential equations with state-dependent delays, transforming them into constant delay systems via time transformations, and compares their asymptotic behaviors.

Contribution

It introduces a method to convert state-dependent delay systems into constant delay systems using time transformations, enabling easier analysis.

Findings

Transformation preserves asymptotic properties

Constant delay systems are easier to analyze

Comparison shows similar long-term behavior

Abstract

Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant delay systems and compare the asymptotic properties of the original and transformed systems.