In excitable systems, superthreshold stimuli can cause strong responses—events. Event generation is often modulated by slow feedback processes. The interplay of noise and a positive (upregulating) event-triggered feedback mechanism in excitable systems is studied using the active rotator (AR) model. First, recent results on the dynamics of a single AR with positive feedback are reviewed. Feedback may lead to bursting that results from stochastic switching between a subthreshold and a superthreshold regime. Both regimes coexist in a limited range of noise intensities. Second, novel results on all-to-all coupled ARs in the presence of positive feedback are presented. The interplay of noise, feedback, and input from other ARs can lead to asynchronous bursting of individual elements and collective bursting of the entire network. Collective event generation is strongly shaped by the network size. For a fixed noise intensity, sparse collective event generation is observed in large networks, while small networks exhibit rapid collective event generation. Collective bursting occurs for intermediate network sizes. The presented results contribute to a deeper understanding of the complex interplay of noise and slow feedback processes in interacting excitable systems.

在可兴奋系统中，超阈值刺激可以引起强烈的反应——事件。事件生成通常由缓慢的反馈过程调制。使用主动旋转器 (AR) 模型研究了可兴奋系统中噪声与正（上调）事件触发反馈机制的相互作用。首先，回顾了具有正反馈的单个 AR 动力学的最新结果。反馈可能导致突发，这是由于亚阈值和超阈值机制之间的随机切换造成的。这两种制度在有限的噪声强度范围内共存。其次，提出了在存在正反馈的情况下对所有耦合 AR 的新结果。来自其他 AR 的噪声、反馈和输入的相互作用可能导致单个元素的异步爆发和整个网络的集体爆发。集体事件的产生很大程度上受网络规模的影响。对于固定的噪声强度，在大型网络中观察到稀疏的集体事件生成，而小型网络则表现出快速的集体事件生成。中间网络规模发生集体突发。所呈现的结果有助于更深入地了解相互作用的可兴奋系统中噪声和缓慢反馈过程的复杂相互作用。