Generalized stochastic resonance of the harmonic oscillator with Mittag–Leffler memory kernel and time delay

Yan Tian

Physica A: Statistical Mechanics and its Applications, 2025, vol. 669, issue C

Abstract: In this study, we introduce a fluctuating-mass harmonic oscillator with Mittag-Leffler memory kernel and time delay. Firstly, we derive the exact analytical expression of output amplitude gain (OAG) using moment method. Then, we observe the generalized stochastic resonance (GSR) in the system based on the expression. We further examine how GSR behavior depends on system parameters, and discuss the similarities and differences of GSR behavior between Mittag-Leffler memory kernel and classical power-law memory kernel. We demonstrate time delay, the characteristic memory time and the memory exponent are crucial in facilitating its resonance form and optimizing its intensity. In particular, the resonance intensity could quickly enhanced by tuning the above parameters, which has important application in some fields such as signal detection. Finally, we verify the accuracy of the analytical result using numerical simulations.

Keywords: Generalized stochastic resonance; Mittag–Leffler memory kernel; Time delay; Fluctuating mass (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:669:y:2025:i:c:s037843712500233x

DOI: 10.1016/j.physa.2025.130581

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