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Phase synchronization of chaos is studied using a modified R\"ossler system. By employing a lift of the phase variable (i.e., phase points separated by 2π are not considered as the same), the transition to phase synchronization is viewed as a boundary crisis mediated by an unstable-unstable pair bifurcation on a branched manifold, and the accompanying basin boundary structure is found to be of a new type.
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Rosa et al. (1998) studied this question.
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