  We investigate phase transitions towards frequency entrainment in large,
locally coupled networks of limit cycle oscillators. Specifically, we simulate
two-dimensional lattices of pulse-coupled oscillators with random natural
frequencies, resembling pacemaker cells in the heart. As coupling increases,
the system seems to undergo two phasetransitions in the thermodynamic limit. At
the first, the largest cluster of frequency entrained oscillators becomes
macroscopic. At the second, global entrainment settles. Between the two
transitions, the system has features indicating self-organized criticality.
