Prevalence of unstable attractors in networks of pulse-coupled oscillators

We present and analyze the first example of a dynamical system that naturally exhibits attracting periodic orbits that are $\mathit{\text{unstable}}$. These unstable attractors occur in networks of pulse-coupled oscillators where they prevail for large networks and a wide range of parameters. They are enclosed by basins of attraction of other attractors but are remote from their own basin volume such that arbitrarily small noise leads to a switching among attractors.