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We study numerically the oscillation death state in the phase oscillatormodel proposed byWinfree. We found that the phases in this state follow verysimple rules, actually, besides intrinsic properties of the oscillators, suchas natural frequency and pulse shape, they depend only on the inverse of thedegree. Other topological properties such as transitivity or associativityseems to play no role on this state. Furthermore, we found thatdegree-frequency correlation helps to inhibit oscillation death. Simpleanalytical approximations corroborate the numerical results.

Approximate solution for the oscillation death state in pulse coupled oscillators