The remarkable phenomenon of chimera state in systems of non-locally coupled, identical oscillators has attracted a great deal of recent theoretical and experimental interests. In such a state, different groups of oscillators can exhibit characteristically distinct types of dynamical behaviors, in spite of identity of the oscillators. But how robust are chimera states against random perturbations to the structure of the underlying network? We address this fundamental issue by studying the effects of random removal of links on the probability for chimera states. Using direct numerical calculations and two independent theoretical approaches, we find that the likelihood of chimera state decreases with the probability of random-link removal. A striking finding is that, even when a large number of links are removed so that chimera states are deemed not possible, in the state space there are generally both coherent and incoherent regions. The regime of chimera state is a particular case in which the oscillators in the coherent region happen to be synchronized or phase-locked.
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