In traditional viewpoint, excitatory modulation always promotes neural firing activities. On contrary, the negative responses of complex bursting behaviors to excitatory self-feedback mediated by autapse with time delay are acquired in the present paper. Two representative bursting patterns which are identified respectively to be “Fold/Big Homoclinic” bursting and “Circle/Fold cycle” bursting with bifurcations are studied. For both burstings, excitatory modulation can induce less spikes per burst for suitable time delay and strength of the self-feedback/autapse, because the modulation can change the initial or termination phases of the burst. For the former bursting composed of quiescent state and burst, the mean firing frequency exhibits increase, due to that the quiescent state becomes much shorter than the burst. However, for the latter bursting pattern with more complex behavior which is depolarization block lying between burst and quiescent state, the firing frequency manifests decrease in a wide range of time delay and strength, because the duration of both depolarization block and quiescent state becomes long. Therefore, the decrease degree of spike number per burst is larger than that of the bursting period, which is the cause for the decrease of firing frequency. Such reduced bursting activity is explained with the relations between the bifurcation points of the fast subsystem and the bursting trajectory. The present paper provides novel examples of paradoxical phenomenon that the excitatory effect induces negative responses, which presents possible novel modulation measures and potential functions of excitatory self-feedback/autapse to reduce bursting activities.

在传统观点中，兴奋性调制总是促进神经放电活动。相反，本文获得了复杂的爆发行为对由时延自动调节介导的兴奋性自我反馈的负面反应。研究了两种具有代表性的爆破模式，分别是“折叠/大同宿”爆破和“圆/折叠循环”分叉爆破。对于这两种爆发，兴奋性调制可以在适当的时间延迟和自反馈/自动响应的强度下，每次爆发产生更少的尖峰，因为调制可以改变爆发的初始或终止阶段。对于由静止状态和爆发组成的前爆发，平均发射频率表现出增加，因为静止状态变得比爆发短得多。然而，对于后一种具有更复杂行为的爆发模式，即位于爆发和静止状态之间的去极化阻滞，由于去极化阻滞和静止状态的持续时间都变长，因此放电频率在很宽的时间延迟和强度范围内表现出降低。因此，每个脉冲的脉冲数减少程度大于脉冲周期的减少程度，这是点火频率降低的原因。这种减少的爆发活动可以用快速子系统的分叉点与爆发轨迹之间的关系来解释。本文提供了矛盾现象的新例子，即兴奋效应引起负面反应，