Convergence to square waves for a price model with delay

Hans-Otto Walther

doi:10.3934/dcds.2005.13.1325

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2005, Volume 13, Issue 5: 1325-1342. Doi: 10.3934/dcds.2005.13.1325

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Convergence to square waves for a price model with delay

Hans-Otto Walther^1,

1.
Mathematisches Institut, Universität Gieβen, Arndtstr. 2, 35392 Gieβen

Received: July 31, 2004

Revised: March 31, 2005

Published: September 2005

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Abstract

It is shown that periodic solutions of a delay differential equation approach a square wave if a parameter becomes large. The equation models short-term prize fluctuations. The proof relies on the fact that the branches of the unstable manifold at equilibrium tend to the periodic orbit.

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Mathematics Subject Classification: Primary: 34K13, 34K15; Secondary: 37L99, 91B24.

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