Phase transitions towards frequency entrainment in large oscillator lattices.

We simulate two-dimensional lattices of pulse-coupled oscillators with random natural frequencies, resembling pacemaker cells in the heart. As coupling increases, this system seems to undergo two phase transitions in the thermodynamic limit. First, the largest cluster of frequency entrained oscillators becomes macroscopic. Second, all oscillators frequency entrain, except possibly some isolated ones. Between the two transitions, the system has features indicating self-organized criticality. To our knowledge, the first transition and the intermediate phase have never been observed before. It remains to be seen if they are generic for large lattices of limit cycle oscillators.