Phase transitions in mixed populations composed of two types of self-oscillatory elements with different periods

In globally coupled networks composed of oscillatory and nonoscillatory elements, the balance between the subpopulations plays an important role in network dynamics and phase transitions. To extend this framework, we investigate mixed populations consisting of two types of self-oscillatory elements with different periods, particularly given by limit cycle oscillators and period-doubled ones. Phase transitions in the mixed populations are elucidated by numerical bifurcation analyses of a reduced system. We numerically confirm a formula determining the critical balance between the subpopulations for a phase transition at sufficiently large coupling strength.