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Phase Transitions in Complex Networks of Active and Inactive Oscillators

Gouhei Tanaka, Kai Morino, Kazuyuki Aihara
We study phase transitions in mixed populations of interacting active and inactive oscillators on complex networks. As the ratio of inactive oscillators to the total population increases, the macroscopic oscillatory activity of the whole network decreases and eventually stops at a critical ratio. This phase transition, called an aging transition, has been studied with simple networks so far. To extend the conventional framework, we analyze aging transitions in complex networks including random and scale-free networks. The critical ratio is theoretically derived through appropriate approximations and numerically verified.
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