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arXiv · 2411.10105

Parametric Autoresonance with Time-Delayed Control

Somnath Roy·Mattia Coccolo·Miguel A. F. Sanjuán
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Abstract

We investigate how a constant time delay influences a parametric autoresonant system. This is a nonlinear system driven by a parametrically chirped force with a negative delay-feedback that maintains adiabatic phase locking with the driving frequency. This phase locking results in a continuous amplitude growth, regardless of parameter changes. Our study reveals a critical threshold for delay strength; above this threshold, autoresonance is sustained, while below it, autoresonance diminishes. We examine the interplay between time delay and autoresonance stability, using multi-scale perturbation methods to derive analytical results, which are corroborated by numerical simulations. Ultimately, the goal is to understand and control autoresonance stability through the time-delay parameters.

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Somnath Roy, Mattia Coccolo, Miguel A. F. Sanjuán. 2024-11-15. Parametric Autoresonance with Time-Delayed Control. https://arxiv.org/abs/2411.10105

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