In [Viktorov M E et al. 2016 Eur. Phys. Lett. 116 55001] we reported on chirping frequency patterns that have been observed in the electron cyclotron emission from strongly nonequilibrium plasma confined in a table-top mirror magnetic trap. These patterns were interpreted qualitatively as the first experimental evidence for so-called "holes and clumps" mechanism acting at such high frequencies (1-10 GHz). In the present paper, we prove this statement on a more rigorous basis, considering the formation of nonlinear phase space structures in proximity of the wave-particle resonances within the framework of the Berk-Breizman theory adopted for a kinetically unstable mirror-confined plasma.