Dynamics of a large ring of coupled active and inactive oscillators

A system of coupled oscillators may include inactive elements that have lost spontaneous oscillatory activity for some reason, such as aging and accidental damages. Following previous papers devoted to the case of global coupling, here the discussion is centered around what happens in a large ring of locally coupled oscillators, some of which are inactivated. In particular, it is shown that the critical ratio of inactive oscillators at which the system makes a transition to quiescence approaches unity algebraically as the system size tends to infinity. It is also shown that under some conditions, the system's phase coherence is enhanced by intensifying quenched disorder originating from random assignments of inactive sites on the ring.