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Deadlocks in the synchronization of pulse-coupled oscillators on star graphs.

Some convergence proofs for systems of oscillators with inhibitory pulse coupling assume that all initial phases reside in one half of their domain. A violation of this assumption can trigger deadlocks that prevent synchronization. We analyze the conditions for such deadlocks in star graphs, characterizing the domain of initial states leading to deadlocks and deriving its fraction of the state space. The results show that convergence is feasible from a wider range of initial phases. The same type of deadlock occurs in random graphs.