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

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  • Tian, Yan

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.

Suggested Citation

  • Tian, Yan, 2025. "Generalized stochastic resonance of the harmonic oscillator with Mittag–Leffler memory kernel and time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 669(C).
    • Handle: RePEc:eee:phsmap:v:669:y:2025:i:c:s037843712500233x
    DOI: 10.1016/j.physa.2025.130581
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    References listed on IDEAS

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    1. Tian, Yan & Yu, Tao & He, Gui-Tian & Zhong, Lin-Feng & Stanley, H. Eugene, 2020. "The resonance behavior in the fractional harmonic oscillator with time delay and fluctuating mass," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
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    7. Tian, Yan & He, Guitian & Liu, Zhibin & Zhong, Linfeng & Yang, Xinping & Stanley, H. Eugene & Tu, Zhe, 2021. "The impact of memory effect on resonance behavior in a fractional oscillator with small time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).
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