Dynamic phase transitions in the kinetic spin-1 Blume-Capel model on the Bethe lattice

► In this paper we have studied a kinetic spin-1 Ising model on the Bethe lattice. ► The dynamic order parameters are calculated. ► Paramagnetic (P), ferromagnetic (F) and (F+P) phases are found. ► The model presents second-order and first-order phase transitions. ► Dynamic tricritical and dynamic triple points are also observed.