Identification of dynamics of the mixed-mode oscillations (MMOs), which exhibit transition between oscillations with large and small amplitudes, is very important for nonlinear physics. In this paper, the MMOs with transition between subthreshold oscillations and spikes are investigated in a neuron model. In the absence of noise, the MMOs appear between the resting state and period-1 firing with increasing depolarization current. After introducing white noise, coherence resonance (CR) is evoked from the resting state and non-CR is induced from period-1 firing far from the MMOs, which is consistent with the traditional viewpoint. However, an interesting result that a transition from anti-CR to CR is evoked by noise from both the MMOs and the period-1 firing near the MMOs is acquired, which is characterized by the increase, decrease and increase again of the coefficient of variations of interspike intervals (ISIs) with increasing noise intensity. At small noise intensity, more subthreshold oscillations are evoked by noise to reduce the firing frequency, resulting in faster increase of standard deviation (SD) of ISIs than that of mean value of ISIs, which is the cause for the anti-CR. The decrease of SD is faster for middle noise intensity and is lower for strong noise intensity, which is the cause for the CR. The different stochastic responses of MMOs and period-1 firing nearby at different levels of noise insanity are the dynamical mechanism for the transition from anti-CR to CR. Such results present potential functions of the MMOs and period-1 firing on information processing in the nervous system with noise and extend the conditions for the CR and anti-CR phenomena, which enriches the contents of nonlinear dynamics.

中文翻译：

---

从反相干共振过渡到混合模式振荡和神经系统第一周期放电的相干共振

识别混合模式振荡 (MMO) 的动力学，它表现出大振幅和小振幅的振荡之间的过渡，对于非线性物理学非常重要。在本文中，在神经元模型中研究了在亚阈值振荡和尖峰之间转换的 MMO。在没有噪声的情况下，随着去极化电流的增加，MMO 出现在静止状态和第 1 期放电之间。引入白噪声后，从静止状态诱发相干共振（CR），从远离MMO的第1期发射诱发非CR，这与传统观点一致。然而，获得了一个有趣的结果，即从反 CR 到 CR 的过渡是由 MMO 和 MMO 附近的第 1 期发射的噪声引起的，其特征是增加，随着噪声强度的增加，峰间间隔 (ISI) 的变异系数减小并再次增大。在较小的噪声强度下，噪声引起更多的阈下振荡以降低发射频率，导致ISI的标准偏差（SD）比ISI的平均值增加得更快，这是抗CR的原因。中等噪声强度的SD下降较快，强噪声强度的SD下降较慢，这就是CR的原因。MMOs的不同随机响应和在不同噪声级别附近发射的第1周期是从反CR过渡到CR的动力学机制。