The dynamics responsible for lifting the degeneracy of the Landau levels in the quantum Hall (QH) effect in graphene is studied by utilizing a low-energy effective model with a contact interaction. A detailed analysis of the solutions of the gap equation for Dirac quasiparticles is performed at both zero and nonzero temperatures. The characteristic feature of the solutions is that the order parameters connected with the QH ferromagnetism and magnetic catalysis scenarios necessarily coexist. The solutions reproduce correctly the experimentally observed QH plateaus in graphene in strong magnetic fields. The phase diagram of this system in the plane of temperature and electron chemical potential is analyzed. The phase transitions corresponding to the transitions between different QH plateaus in graphene are described.