Towards a model of population of astrophysical sources of ultra-high-energy cosmic rays

We construct and discuss a toy model of the population of numerous non-identical extragalactic sources of ultra-high-energy cosmic rays. In the model, cosmic-ray particles are accelerated in magnetospheres of supermassive black holes in galactic nuclei, the key parameter of acceleration being the black-hole mass. We use astrophysical data on the redshift-dependent black-hole mass function to describe the population of these cosmic-ray accelerators, from weak to powerful, and confront the model with cosmic-ray data.