Bogdanov–Takens resonance in time-delayed systems
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.
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.
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