Although the bursting patterns with spike undershoot are involved with the achievement of physiological or cognitive functions of brain with synaptic noise, noise induced-coherence resonance (CR) from resting state or subthreshold oscillations instead of bursting has been widely identified to play positive roles in information process. Instead, in the present paper, CR characterized by the increase firstly and then decease of peak value of power spectrum of spike trains is evoked from a bursting pattern with spike undershoot, which means that the minimal membrane potential within burst is lower than that of the subthreshold oscillations between bursts, while CR cannot be evoked from the bursting pattern without spike undershoot. With bifurcations and fast-slow variable dissection method, the bursting patterns with and without spike undershoot are classified into “Sub-Hopf/Fold” bursting and “Fold/Homoclinic” bursting, respectively. For the bursting with spike undershoot, the trajectory of the subthreshold oscillations is very close to that of the spikes within burst. Therefore, noise can induce more spikes from the subthreshold oscillations and modulate the bursting regularity, which leads to the appearance of CR. For the bursting pattern without spike undershoot, the trajectory of the quiescent state is not close to that of the spikes within burst, and noise cannot induce spikes from the quiescent state between bursts, which is cause for non-CR. The result provides a novel case of CR phenomenon and extends the scopes of CR concept, presents that noise can enhance rather than suppress information of the bursting patterns with spike undershoot, which are helpful for understanding the dynamics and the potential physiological or cognitive functions of the nerve fiber or brain neurons with such bursting patterns.

尽管具有尖峰下冲的突发模式与突触噪声实现大脑的生理或认知功能有关，但来自静息状态或阈下振荡而不是突发的噪声诱导相干共振（CR）已被广泛认为在信息中发挥积极作用过程。相反，在本文中，以脉冲序列功率谱峰值先增大后减小为特征的 CR 是由具有脉冲下冲的突发模式诱发的，这意味着突发内的最小膜电位低于脉冲序列的最小膜电位。突发之间的亚阈值振荡，而在没有尖峰下冲的情况下，不能从突发模式中诱发 CR。采用分岔法和快慢变剖分法，有和没有尖峰下冲的突发模式分别分为“Sub-Hopf/Fold”突发和“Fold/Homoclinic”突发。对于具有尖峰下冲的突发，阈下振荡的轨迹非常接近突发内尖峰的轨迹。因此，噪声可以从亚阈值振荡中引起更多的尖峰，并调节突发规律，从而导致 CR 的出现。对于没有尖峰下冲的突发模式，静止状态的轨迹与突发内的尖峰轨迹不接近，噪声不能从突发之间的静止状态诱导尖峰，这是非CR的原因。该结果提供了一个新的 CR 现象案例并扩展了 CR 概念的范围，