Strong-coupling limit in heterogeneous populations of coupled oscillators

Coupled oscillators can be heterogeneous in the sense that parameter values of constituent oscillators are not uniform for various reasons. Here it is discussed how such a system behaves in the strong-coupling limit. A theory is developed under certain assumptions and then used to quite generally explain an empirical law about a phase transition boundary in a class of heterogeneous populations of coupled oscillators such that bifurcation parameters are distributed. Results obtained here will be useful as a starting point for studying the behavior of such systems for moderate coupling strengths.