We study evolution of a hierarchical four-body (2+2) system composed by a pair of mass-transferring white dwarf binaries. Applying a simplified model around the synchronous state of two inner orbital periods, we newly find that the four body system could settle down to a limit cycle with a small period gap. The period gap generates an amplitude variation of emitted gravitational waves, as a beat effect. Depending on model parameters, the beat period could be 1-10 yr and a large amplitude variation might be observed by space gravitational-wave detectors.
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