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This paper investigates the constraints placed on somesynchronized oscillator models by their underlying dynamics. Phaseresponse graphs are used to determine the phase locking behaviorsof three oscillator models. These results are compared withidealized phase response graphs for single phase and multiple phasesystems. We find that all three oscillators studied are best suitedto operate in a single phase system and that the requirementsplaced on oscillatory models for operation in a multiple phasesystem are not compatible with the underlying dynamics ofoscillatory behavior for these types of oscillator models.