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Bifurcation to large period oscillations in physical systems controlled by delay

par Erneux, Thomas ;Walther, H. O.
Référence Physical Review E (Statistical, Nonlinear, and Soft Matter Physics), 72, page (066206)
Publication Publié, 2005

Article révisé par les pairs

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Résumé :

An unusual bifurcation to time-periodic oscillations of a class of delay differential equations is investigated. As we approach the bifurcation point, both the amplitude and the frequency of the oscillations go to zero. The class of delay differential equations is a nonlinear extension of a nonevasive control method and is motivated by a recent study of the foreign exchange rate oscillations. By using asymptotic methods, we determine the bifurcation scaling laws for the amplitude and the period of the oscillations.