This paper aims to explore the Lévy noise-induced effects in underdamped asymmetric bistable system. Lévy noise is generated by Janicki–Weron algorithm which is different from the usual Gaussian noise. The numerical solutions of system equation are obtained by the fourth-order stochastic Runge–Kutta algorithm. Then the quasi-steady-state probability density (QSPD) is obtained by solving the equation of system, and the stochastic resonance (SR) is determined by the classical measure of signal-to-noise ratio (SNR). The influence of various parameters of the Lévy noise and the system parameters on QSPD and SNR is discussed. Noise-induced transitions occur by varying the parameters of the Lévy noise and the driven system. Moreover, within certain limits, the larger value of the stability index [Formula: see text] of Lévy noise, signal amplitude [Formula: see text], and the absolute values of asymmetric parameter [Formula: see text] can give rise to the SR phenomenon. On the contrary, the larger values of skewness parameters [Formula: see text] of Lévy noise and damping parameter [Formula: see text] further weaken the occurrence of the SR phenomenon in the given system.

中文翻译：

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欠阻尼非对称双稳态系统中的 Lévy 噪声诱导效应

本文旨在探讨欠阻尼不对称双稳态系统中的 Lévy 噪声诱导效应。Lévy 噪声是由 Janicki-Weron 算法产生的，它不同于通常的高斯噪声。系统方程的数值解由四阶随机Runge-Kutta算法得到。然后通过求解系统方程得到准稳态概率密度（QSPD），并通过经典的信噪比（SNR）度量确定随机共振（SR）。讨论了 Lévy 噪声的各种参数和系统参数对 QSPD 和 SNR 的影响。通过改变 Lévy 噪声和驱动系统的参数，会发生噪声引起的过渡。此外，在一定限度内，Lévy 噪声的稳定性指标 [公式：见正文] 的较大值，信号幅度[公式：见正文]，不对称参数的绝对值[公式：见正文]会引起SR现象。相反，较大的 Lévy 噪声偏度参数 [公式：见正文] 和阻尼参数 [公式：见正文] 进一步削弱了给定系统中 SR 现象的发生。