The noise-induced dynamics of the oscillator, which is of an excitable potential and positive dissipation, is investigated in this paper. As a noise-induced coherence behavior, the self-induced stochastic resonance (SISR) caused by small random perturbations is explored in numerical simulations. It is found that when noise is small and finite, the location of the limit cycle induced by the SISR can be better determined when the prefactor of the WKB approximation of the Kramers rate is considered. Besides, unlike other excitable systems, only confined to a very small noise interval, the regular limit cycles induced by the SISR can be observed.

中文翻译：

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可激发势阱中的自诱导随机共振

本文研究了振荡器的噪声引起的动力学，它具有可激发的电位和正耗散。作为噪声诱导的相干行为，在数值模拟中探索了由小随机扰动引起的自诱导随机共振 (SISR)。研究发现，当噪声较小且有限时，考虑Kramers率的WKB近似值的前置因子，可以更好地确定SISR引起的极限环的位置。此外，与其他可激励系统不同，仅局限于非常小的噪声区间，可以观察到由 SISR 引起的规则极限循环。