We discuss the situation where two periodic signals compete to phase synchronize a chaotic attractor. Depending on the relative position of the periods with respect to the synchronization tongue for a single frequency signal, we distinguish several different cases. We find that, depending on parameters, it is possible that one or the other signal will entrain exclusively, or that they will entrain alternately, at their average frequency, or not at all.

• Received 1 October 2001

DOI:https://doi.org/10.1103/PhysRevE.65.056219