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

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  • Houyu Zhao

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 constant λ at resonance, that is, at a root of the unity, but also those λ near resonance under the Brjuno condition.

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Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:180595
DOI: 10.1155/2012/180595
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