Analytic Solutions for a Functional Differential Equation Related to a Traffic Flow Model

Abstract

We study the existence of analytic solutions of a functional differential equation(z(s)+α)2z'(s)=β(z(s+z(s))-z(s))which comes from traffic flow model. By reducing the equation with the Schröder transformation to an auxiliary equation, the author discusses not only that the constantλat resonance, that is, at a root of the unity, but also thoseλnear resonance under the Brjuno condition.