Convergence to square waves for a price model with delay

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October 2005, 13(5): 1325-1342. doi: 10.3934/dcds.2005.13.1325

Convergence to square waves for a price model with delay

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

Received August 2004 Revised April 2005 Published September 2005

Abstract
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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.

Keywords: Delay differential equation, periodic solution, square wave, limiting profile..

Mathematics Subject Classification: Primary: 34K13, 34K15; Secondary: 37L99, 91B2.

Citation: Hans-Otto Walther. Convergence to square waves for a price model with delay. Discrete & Continuous Dynamical Systems - A, 2005, 13 (5) : 1325-1342. doi: 10.3934/dcds.2005.13.1325

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