Noise-induced dynamics of coupled excitable systems with slow positive feedback

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.