Abstract
Energetic and entropic vibrational resonance with a time-delayed feedback is studied by considering a Brownian particle confined in a two-dimensional boundary. Both the time delay and high-frequency signal can optimize the output of the system. The delay time can induce the multimodal resonance with a local optimum peak in the spectral amplification factor. Furthermore, the mechanism corresponded to dynamical transition from a multi-stable state to a monostable state caused by the high-frequency signal is elucidated. In addition, a quantity called the mean entropic Poisson intensity is employed, which can be used to assist in describing the constraint effects of uneven boundaries. It is worth mentioning that this quantity can also properly describe the vibrational resonance of the system. Finally, our work provides some theoretical references for the detection of weak signals in small-scale systems with ubiquitous fluctuation and time delay.
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