Abstract
A delay differential equation is presented which models how the behavior of traders influences the short time price movements of an asset. Sensitivity to price changes is measured by a parameter a. There is a single equilibrium solution, which is non-hyperbolic for all a>0. We prove that for a< 1 the equilibrium is asymptotically stable, and that for a>1 a 2-dimensional global center-unstable manifold connects the equilibrium to a periodic orbit. Its birth at a=1 is not of Hopf type and seems part of a Takens–Bogdanov scenario.
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An erratum to this article is available at http://dx.doi.org/10.1007/s10884-006-9062-x.
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Brunovský, P., Erdélyi, A. & Walther, HO. On a Model of a Currency Exchange Rate – Local Stability and Periodic Solutions. Journal of Dynamics and Differential Equations 16, 393–432 (2004). https://doi.org/10.1007/s10884-004-4285-1
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DOI: https://doi.org/10.1007/s10884-004-4285-1