Abstract

We analyze the oscillatory dynamics of a time-delayed dynamical system subjected to a periodic external forcing. We show that, for certain values of the delay, the response can be greatly enhanced by a very small forcing amplitude. This phenomenon is related to the presence of a Bogdanov–Takens bifurcation and displays some analogies to other resonance phenomena, but also substantial differences.

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Volume Title

Publisher

SpringerLink

URI

https://hdl.handle.net/10115/32164

DOI

https://doi.org/10.1007/s11071-017-3992-1

Date

2017-12-19

Description

The study investigates the oscillatory behavior of a dynamical system with time delay under periodic external forcing. It reveals that specific delay values can significantly amplify the system's response even with a minimal external force. This phenomenon is attributed to the presence of a Bogdanov-Takens bifurcation. While it shares similarities with other resonance phenomena, it also exhibits notable differences.

Keywords

Nonlinear Dynamics , Bifurcation , resonance , El niño oscillator , Delay

Citation

Coccolo, M., Zhu, B., Sanjuán, M.A.F. et al. Bogdanov–Takens resonance in time-delayed systems. Nonlinear Dyn 91, 1939–1947 (2018). https://doi.org/10.1007/s11071-017-3992-1

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