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Rapid Repetition Rate Fluctuation Measurement of Soliton Crystals in a Microresonator

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Published on: December 15, 2021

Controlling vibrational resonance in a multistable system by time delay.

J H Yang¹, X B Liu

¹Institute of Vibration Engineering Research, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, People's Republic of China. jianhuayang@nuaa.edu.cn

Chaos (Woodbury, N.Y.)

|October 5, 2010

Summary

Time delay controls vibrational resonance in multistable systems excited by biharmonic signals. This new method allows for controlling resonance and orbital motion, offering a novel approach for system manipulation.

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Area of Science:

Nonlinear Dynamics
Chaos Theory
Complex Systems

Background:

Vibrational resonance is a phenomenon in nonlinear systems.
Previous research focused on high-frequency signal amplitude modulation.
Multistable systems exhibit multiple stable states.

Purpose of the Study:

Investigate vibrational resonance in delayed multistable systems under biharmonic excitation.
Explore the control of resonance and orbital motion using time delay.
Analyze the mechanism of delay-induced multiple vibrational resonance.

Main Methods:

Numerical simulations were employed.
Analytical analysis was conducted.
Biharmonic signals were used for excitation.

Main Results:

Time delay, not high-frequency amplitude, controls the onset and disappearance of vibrational resonance.
Orbital motion within and between potential wells is controllable via time delay.
Delay-induced multiple vibrational resonance exhibits periodicity with respect to the delay parameter.

Conclusions:

Time delay offers a novel method for controlling vibrational resonance in multistable systems.
The findings provide new insights into the dynamics of delayed nonlinear systems.
This research opens avenues for manipulating complex system behaviors.