Periodic external input tunes the stability of delayed nonlinear systems: from the slaving principle to center manifolds

Axel Hutt 1 Jérémie Lefebvre 2
1 NEUROSYS - Analysis and modeling of neural systems by a system neuroscience approach
Inria Nancy - Grand Est, LORIA - AIS - Department of Complex Systems, Artificial Intelligence & Robotics
Abstract : The work illustrates a recent analysis technique that demon- strates that external periodic input affects the stability of the time- averaged nonlinear dynamics of a delayed system. At first, the article introduces the fundamental elements of delayed differential equations and then applies these to a nonlinear delayed problem close to a trans- critical bifurcation. We observe a shift of stability in the system induced by the fast periodic driving.
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Axel Hutt, Jérémie Lefebvre. Periodic external input tunes the stability of delayed nonlinear systems: from the slaving principle to center manifolds. 2013. ⟨hal-00912418⟩

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