  We present the first astrophysical application of the ECHO code in its recent
version supplemented by a generalized Ohm law, namely a kinematic study of
dynamo effects in thick accretion disks. High-order \emph{implicit-explicit}
Runge-Kutta time-stepping routines are implemented and validated within $3+1$
\emph{General Relativistic MagnetoHydroDynamics} (GRMHD). The scheme is applied
to a differentially rotating torus orbiting a Kerr black hole, where the
mean-field dynamo process leads to strong amplification of seed magnetic
fields. We show that the interplay between the toroidal and poloidal components
occurs qualitatively in the same fashion as in the Sun, butterfly diagrams are
reproduced, and a typical time-scale for the field evolution is found,
depending on the dynamo and resistivity numbers, which could explain
periodicities as observed in several accreting systems.
