In this paper, the phenomena of coherence resonance (CR) and stochastic resonance (SR) are studied in an asymmetric tri-stable potential with memory effects, which is driven by internal noise and a periodic forcing. Analytical expressions for characteristic correlation time and spectral amplification are derived to quantify the CR and the SR, respectively. The obtained results indicate the existence of a critical value of asymmetry for the onset of CR. For intermediate memory times, there exhibits an optimal memory intensity at which the CR attains maximum. Moreover, memory plays a significant role in an enhancement of CR and SR, which also depends prominently on the tri-stable potential structure. Interestingly, memory time suppresses CR but enhances SR. Specifically, the appropriate choice of asymmetry constant and nonlinear stiffness coefficient can improve the performance of system response to an external periodic signal based on the SR effect. Finally, the results from numerical simulations well verify the validity of the theoretical analyses.

本文研究了在非对称三稳态势中具有记忆效应的相干共振（CR）和随机共振（SR）现象，这种效应由内部噪声和周期性强迫驱动。推导了特征相关时间和频谱放大的解析表达式，以分别量化CR和SR。获得的结果表明对于CR的发作存在不对称的临界值。对于中间存储时间，在CR达到最大值时表现出最佳的存储强度。此外，记忆在增强CR和SR方面起着重要作用，而CR和SR也主要取决于三稳态电位结构。有趣的是，存储时间可以抑制CR，但可以增强SR。特别，不对称常数和非线性刚度系数的合适的选择可以提高系统响应于基于所述SR作用的外部周期信号的性能。最后，数值模拟的结果很好地验证了理论分析的有效性。